id	sid	tid	token	lemma	pos
en-wikipedia-org-3337	1	1	Nash	nash	JJ
en-wikipedia-org-3337	1	2	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	3	-	-	HYPH
en-wikipedia-org-3337	1	4	Wikipedia	Wikipedia	NNP
en-wikipedia-org-3337	1	5	Nash	Nash	NNP
en-wikipedia-org-3337	1	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	7	From	from	IN
en-wikipedia-org-3337	1	8	Wikipedia	Wikipedia	NNP
en-wikipedia-org-3337	1	9	,	,	,
en-wikipedia-org-3337	1	10	the	the	DT
en-wikipedia-org-3337	1	11	free	free	JJ
en-wikipedia-org-3337	1	12	encyclopedia	encyclopedia	NN
en-wikipedia-org-3337	1	13	Jump	Jump	NNP
en-wikipedia-org-3337	1	14	to	to	IN
en-wikipedia-org-3337	1	15	navigation	navigation	NN
en-wikipedia-org-3337	1	16	Jump	Jump	NNP
en-wikipedia-org-3337	1	17	to	to	TO
en-wikipedia-org-3337	1	18	search	search	NN
en-wikipedia-org-3337	1	19	Solution	solution	NN
en-wikipedia-org-3337	1	20	concept	concept	NN
en-wikipedia-org-3337	1	21	of	of	IN
en-wikipedia-org-3337	1	22	a	a	DT
en-wikipedia-org-3337	1	23	non	non	JJ
en-wikipedia-org-3337	1	24	-	-	JJ
en-wikipedia-org-3337	1	25	cooperative	cooperative	JJ
en-wikipedia-org-3337	1	26	game	game	NN
en-wikipedia-org-3337	1	27	involving	involve	VBG
en-wikipedia-org-3337	1	28	two	two	CD
en-wikipedia-org-3337	1	29	or	or	CC
en-wikipedia-org-3337	1	30	more	more	JJR
en-wikipedia-org-3337	1	31	players	player	NNS
en-wikipedia-org-3337	1	32	for	for	IN
en-wikipedia-org-3337	1	33	given	give	VBN
en-wikipedia-org-3337	1	34	conditions	condition	NNS
en-wikipedia-org-3337	1	35	Nash	Nash	NNP
en-wikipedia-org-3337	1	36	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	37	A	a	DT
en-wikipedia-org-3337	1	38	solution	solution	NN
en-wikipedia-org-3337	1	39	concept	concept	NN
en-wikipedia-org-3337	1	40	in	in	IN
en-wikipedia-org-3337	1	41	game	game	NN
en-wikipedia-org-3337	1	42	theory	theory	NN
en-wikipedia-org-3337	1	43	Relationship	Relationship	NNP
en-wikipedia-org-3337	1	44	Subset	Subset	NNP
en-wikipedia-org-3337	1	45	of	of	IN
en-wikipedia-org-3337	1	46	Rationalizability	Rationalizability	NNP
en-wikipedia-org-3337	1	47	,	,	,
en-wikipedia-org-3337	1	48	Epsilon	Epsilon	NNP
en-wikipedia-org-3337	1	49	-	-	HYPH
en-wikipedia-org-3337	1	50	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	51	,	,	,
en-wikipedia-org-3337	1	52	Correlated	correlate	VBN
en-wikipedia-org-3337	1	53	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	54	Superset	superset	NN
en-wikipedia-org-3337	1	55	of	of	IN
en-wikipedia-org-3337	1	56	Evolutionarily	evolutionarily	RB
en-wikipedia-org-3337	1	57	stable	stable	JJ
en-wikipedia-org-3337	1	58	strategy	strategy	NN
en-wikipedia-org-3337	1	59	,	,	,
en-wikipedia-org-3337	1	60	Subgame	Subgame	NNP
en-wikipedia-org-3337	1	61	perfect	perfect	JJ
en-wikipedia-org-3337	1	62	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	63	,	,	,
en-wikipedia-org-3337	1	64	Perfect	perfect	JJ
en-wikipedia-org-3337	1	65	Bayesian	bayesian	JJ
en-wikipedia-org-3337	1	66	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	67	,	,	,
en-wikipedia-org-3337	1	68	Trembling	tremble	VBG
en-wikipedia-org-3337	1	69	hand	hand	NN
en-wikipedia-org-3337	1	70	perfect	perfect	JJ
en-wikipedia-org-3337	1	71	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	72	,	,	,
en-wikipedia-org-3337	1	73	Stable	Stable	NNP
en-wikipedia-org-3337	1	74	Nash	Nash	NNP
en-wikipedia-org-3337	1	75	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	76	,	,	,
en-wikipedia-org-3337	1	77	Strong	Strong	NNP
en-wikipedia-org-3337	1	78	Nash	Nash	NNP
en-wikipedia-org-3337	1	79	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	80	,	,	,
en-wikipedia-org-3337	1	81	Cournot	Cournot	NNP
en-wikipedia-org-3337	1	82	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	83	Significance	significance	NN
en-wikipedia-org-3337	1	84	Proposed	propose	VBN
en-wikipedia-org-3337	1	85	by	by	IN
en-wikipedia-org-3337	1	86	John	John	NNP
en-wikipedia-org-3337	1	87	Forbes	Forbes	NNP
en-wikipedia-org-3337	1	88	Nash	Nash	NNP
en-wikipedia-org-3337	1	89	Jr.	Jr.	NNP
en-wikipedia-org-3337	1	90	Used	use	VBD
en-wikipedia-org-3337	1	91	for	for	IN
en-wikipedia-org-3337	1	92	All	all	DT
en-wikipedia-org-3337	1	93	non	non	JJ
en-wikipedia-org-3337	1	94	-	-	JJ
en-wikipedia-org-3337	1	95	cooperative	cooperative	JJ
en-wikipedia-org-3337	1	96	games	game	NNS
en-wikipedia-org-3337	1	97	In	in	IN
en-wikipedia-org-3337	1	98	game	game	NN
en-wikipedia-org-3337	1	99	theory	theory	NN
en-wikipedia-org-3337	1	100	,	,	,
en-wikipedia-org-3337	1	101	the	the	DT
en-wikipedia-org-3337	1	102	Nash	Nash	NNP
en-wikipedia-org-3337	1	103	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	104	,	,	,
en-wikipedia-org-3337	1	105	named	name	VBN
en-wikipedia-org-3337	1	106	after	after	IN
en-wikipedia-org-3337	1	107	the	the	DT
en-wikipedia-org-3337	1	108	mathematician	mathematician	JJ
en-wikipedia-org-3337	1	109	John	John	NNP
en-wikipedia-org-3337	1	110	Forbes	Forbes	NNP
en-wikipedia-org-3337	1	111	Nash	Nash	NNP
en-wikipedia-org-3337	1	112	Jr.	Jr.	NNP
en-wikipedia-org-3337	1	113	,	,	,
en-wikipedia-org-3337	1	114	is	be	VBZ
en-wikipedia-org-3337	1	115	a	a	DT
en-wikipedia-org-3337	1	116	proposed	propose	VBN
en-wikipedia-org-3337	1	117	solution	solution	NN
en-wikipedia-org-3337	1	118	of	of	IN
en-wikipedia-org-3337	1	119	a	a	DT
en-wikipedia-org-3337	1	120	non	non	JJ
en-wikipedia-org-3337	1	121	-	-	JJ
en-wikipedia-org-3337	1	122	cooperative	cooperative	JJ
en-wikipedia-org-3337	1	123	game	game	NN
en-wikipedia-org-3337	1	124	involving	involve	VBG
en-wikipedia-org-3337	1	125	two	two	CD
en-wikipedia-org-3337	1	126	or	or	CC
en-wikipedia-org-3337	1	127	more	more	JJR
en-wikipedia-org-3337	1	128	players	player	NNS
en-wikipedia-org-3337	1	129	in	in	IN
en-wikipedia-org-3337	1	130	which	which	WDT
en-wikipedia-org-3337	1	131	each	each	DT
en-wikipedia-org-3337	1	132	player	player	NN
en-wikipedia-org-3337	1	133	is	be	VBZ
en-wikipedia-org-3337	1	134	assumed	assume	VBN
en-wikipedia-org-3337	1	135	to	to	TO
en-wikipedia-org-3337	1	136	know	know	VB
en-wikipedia-org-3337	1	137	the	the	DT
en-wikipedia-org-3337	1	138	equilibrium	equilibrium	NN
en-wikipedia-org-3337	1	139	strategies	strategy	NNS
en-wikipedia-org-3337	1	140	of	of	IN
en-wikipedia-org-3337	1	141	the	the	DT
en-wikipedia-org-3337	1	142	other	other	JJ
en-wikipedia-org-3337	1	143	players	player	NNS
en-wikipedia-org-3337	1	144	,	,	,
en-wikipedia-org-3337	1	145	and	and	CC
en-wikipedia-org-3337	1	146	no	no	DT
en-wikipedia-org-3337	1	147	player	player	NN
en-wikipedia-org-3337	1	148	has	have	VBZ
en-wikipedia-org-3337	1	149	anything	anything	NN
en-wikipedia-org-3337	1	150	to	to	TO
en-wikipedia-org-3337	1	151	gain	gain	VB
en-wikipedia-org-3337	1	152	by	by	IN
en-wikipedia-org-3337	1	153	changing	change	VBG
en-wikipedia-org-3337	1	154	only	only	RB
en-wikipedia-org-3337	1	155	their	-PRON-	PRP$
en-wikipedia-org-3337	1	156	own	own	JJ
en-wikipedia-org-3337	1	157	strategy	strategy	NN
en-wikipedia-org-3337	1	158	.	.	.
en-wikipedia-org-3337	2	1	[	[	-LRB-
en-wikipedia-org-3337	2	2	1	1	LS
en-wikipedia-org-3337	2	3	]	]	-RRB-
en-wikipedia-org-3337	2	4	The	the	DT
en-wikipedia-org-3337	2	5	utilization	utilization	NN
en-wikipedia-org-3337	2	6	of	of	IN
en-wikipedia-org-3337	2	7	Nash	Nash	NNP
en-wikipedia-org-3337	2	8	Equilibriums	Equilibriums	NNPS
en-wikipedia-org-3337	2	9	,	,	,
en-wikipedia-org-3337	2	10	and	and	CC
en-wikipedia-org-3337	2	11	its	-PRON-	PRP$
en-wikipedia-org-3337	2	12	principles	principle	NNS
en-wikipedia-org-3337	2	13	date	date	NN
en-wikipedia-org-3337	2	14	data	datum	NNS
en-wikipedia-org-3337	2	15	back	back	RB
en-wikipedia-org-3337	2	16	to	to	IN
en-wikipedia-org-3337	2	17	the	the	DT
en-wikipedia-org-3337	2	18	time	time	NN
en-wikipedia-org-3337	2	19	of	of	IN
en-wikipedia-org-3337	2	20	Cournot	Cournot	NNP
en-wikipedia-org-3337	2	21	,	,	,
en-wikipedia-org-3337	2	22	a	a	DT
en-wikipedia-org-3337	2	23	prominent	prominent	JJ
en-wikipedia-org-3337	2	24	Philosopher	Philosopher	NNP
en-wikipedia-org-3337	2	25	and	and	CC
en-wikipedia-org-3337	2	26	mathematician	mathematician	NN
en-wikipedia-org-3337	2	27	who	who	WP
en-wikipedia-org-3337	2	28	pioneered	pioneer	VBD
en-wikipedia-org-3337	2	29	the	the	DT
en-wikipedia-org-3337	2	30	understanding	understanding	NN
en-wikipedia-org-3337	2	31	of	of	IN
en-wikipedia-org-3337	2	32	economic	economic	JJ
en-wikipedia-org-3337	2	33	equilibria	equilibrium	NNS
en-wikipedia-org-3337	2	34	.	.	.
en-wikipedia-org-3337	3	1	[	[	-LRB-
en-wikipedia-org-3337	3	2	2	2	LS
en-wikipedia-org-3337	3	3	]	]	-RRB-
en-wikipedia-org-3337	3	4	If	if	IN
en-wikipedia-org-3337	3	5	each	each	DT
en-wikipedia-org-3337	3	6	player	player	NN
en-wikipedia-org-3337	3	7	has	have	VBZ
en-wikipedia-org-3337	3	8	chosen	choose	VBN
en-wikipedia-org-3337	3	9	a	a	DT
en-wikipedia-org-3337	3	10	strategy	strategy	NN
en-wikipedia-org-3337	3	11	—	—	:
en-wikipedia-org-3337	3	12	an	an	DT
en-wikipedia-org-3337	3	13	action	action	NN
en-wikipedia-org-3337	3	14	plan	plan	NN
en-wikipedia-org-3337	3	15	choosing	choose	VBG
en-wikipedia-org-3337	3	16	its	-PRON-	PRP$
en-wikipedia-org-3337	3	17	own	own	JJ
en-wikipedia-org-3337	3	18	action	action	NN
en-wikipedia-org-3337	3	19	based	base	VBN
en-wikipedia-org-3337	3	20	on	on	IN
en-wikipedia-org-3337	3	21	what	what	WP
en-wikipedia-org-3337	3	22	it	-PRON-	PRP
en-wikipedia-org-3337	3	23	has	have	VBZ
en-wikipedia-org-3337	3	24	seen	see	VBN
en-wikipedia-org-3337	3	25	happen	happen	VB
en-wikipedia-org-3337	3	26	so	so	RB
en-wikipedia-org-3337	3	27	far	far	RB
en-wikipedia-org-3337	3	28	in	in	IN
en-wikipedia-org-3337	3	29	the	the	DT
en-wikipedia-org-3337	3	30	game	game	NN
en-wikipedia-org-3337	3	31	—	—	:
en-wikipedia-org-3337	3	32	and	and	CC
en-wikipedia-org-3337	3	33	no	no	DT
en-wikipedia-org-3337	3	34	player	player	NN
en-wikipedia-org-3337	3	35	can	can	MD
en-wikipedia-org-3337	3	36	increase	increase	VB
en-wikipedia-org-3337	3	37	its	-PRON-	PRP$
en-wikipedia-org-3337	3	38	own	own	JJ
en-wikipedia-org-3337	3	39	expected	expected	JJ
en-wikipedia-org-3337	3	40	payoff	payoff	NN
en-wikipedia-org-3337	3	41	by	by	IN
en-wikipedia-org-3337	3	42	changing	change	VBG
en-wikipedia-org-3337	3	43	its	-PRON-	PRP$
en-wikipedia-org-3337	3	44	strategy	strategy	NN
en-wikipedia-org-3337	3	45	while	while	IN
en-wikipedia-org-3337	3	46	the	the	DT
en-wikipedia-org-3337	3	47	other	other	JJ
en-wikipedia-org-3337	3	48	players	player	NNS
en-wikipedia-org-3337	3	49	keep	keep	VBP
en-wikipedia-org-3337	3	50	theirs	-PRON-	PRP
en-wikipedia-org-3337	3	51	unchanged	unchanged	JJ
en-wikipedia-org-3337	3	52	,	,	,
en-wikipedia-org-3337	3	53	then	then	RB
en-wikipedia-org-3337	3	54	the	the	DT
en-wikipedia-org-3337	3	55	current	current	JJ
en-wikipedia-org-3337	3	56	set	set	NN
en-wikipedia-org-3337	3	57	of	of	IN
en-wikipedia-org-3337	3	58	strategy	strategy	NN
en-wikipedia-org-3337	3	59	choices	choice	NNS
en-wikipedia-org-3337	3	60	constitutes	constitute	VBZ
en-wikipedia-org-3337	3	61	a	a	DT
en-wikipedia-org-3337	3	62	Nash	Nash	NNP
en-wikipedia-org-3337	3	63	equilibrium	equilibrium	NN
en-wikipedia-org-3337	3	64	.	.	.
en-wikipedia-org-3337	4	1	If	if	IN
en-wikipedia-org-3337	4	2	two	two	CD
en-wikipedia-org-3337	4	3	players	player	NNS
en-wikipedia-org-3337	4	4	Alice	Alice	NNP
en-wikipedia-org-3337	4	5	and	and	CC
en-wikipedia-org-3337	4	6	Bob	Bob	NNP
en-wikipedia-org-3337	4	7	choose	choose	VB
en-wikipedia-org-3337	4	8	strategies	strategy	NNS
en-wikipedia-org-3337	4	9	A	a	NN
en-wikipedia-org-3337	4	10	and	and	CC
en-wikipedia-org-3337	4	11	B	b	NN
en-wikipedia-org-3337	4	12	,	,	,
en-wikipedia-org-3337	4	13	(	(	-LRB-
en-wikipedia-org-3337	4	14	A	a	NN
en-wikipedia-org-3337	4	15	,	,	,
en-wikipedia-org-3337	4	16	B	b	NN
en-wikipedia-org-3337	4	17	)	)	-RRB-
en-wikipedia-org-3337	4	18	is	be	VBZ
en-wikipedia-org-3337	4	19	a	a	DT
en-wikipedia-org-3337	4	20	Nash	Nash	NNP
en-wikipedia-org-3337	4	21	equilibrium	equilibrium	NN
en-wikipedia-org-3337	4	22	if	if	IN
en-wikipedia-org-3337	4	23	Alice	Alice	NNP
en-wikipedia-org-3337	4	24	has	have	VBZ
en-wikipedia-org-3337	4	25	no	no	DT
en-wikipedia-org-3337	4	26	other	other	JJ
en-wikipedia-org-3337	4	27	strategy	strategy	NN
en-wikipedia-org-3337	4	28	available	available	JJ
en-wikipedia-org-3337	4	29	that	that	WDT
en-wikipedia-org-3337	4	30	does	do	VBZ
en-wikipedia-org-3337	4	31	better	well	RBR
en-wikipedia-org-3337	4	32	than	than	IN
en-wikipedia-org-3337	4	33	A	a	DT
en-wikipedia-org-3337	4	34	at	at	IN
en-wikipedia-org-3337	4	35	maximizing	maximize	VBG
en-wikipedia-org-3337	4	36	her	-PRON-	PRP$
en-wikipedia-org-3337	4	37	payoff	payoff	NN
en-wikipedia-org-3337	4	38	in	in	IN
en-wikipedia-org-3337	4	39	response	response	NN
en-wikipedia-org-3337	4	40	to	to	IN
en-wikipedia-org-3337	4	41	Bob	Bob	NNP
en-wikipedia-org-3337	4	42	choosing	choose	VBG
en-wikipedia-org-3337	4	43	B	b	NN
en-wikipedia-org-3337	4	44	,	,	,
en-wikipedia-org-3337	4	45	and	and	CC
en-wikipedia-org-3337	4	46	Bob	Bob	NNP
en-wikipedia-org-3337	4	47	has	have	VBZ
en-wikipedia-org-3337	4	48	no	no	DT
en-wikipedia-org-3337	4	49	other	other	JJ
en-wikipedia-org-3337	4	50	strategy	strategy	NN
en-wikipedia-org-3337	4	51	available	available	JJ
en-wikipedia-org-3337	4	52	that	that	WDT
en-wikipedia-org-3337	4	53	does	do	VBZ
en-wikipedia-org-3337	4	54	better	well	RBR
en-wikipedia-org-3337	4	55	than	than	IN
en-wikipedia-org-3337	4	56	B	b	NN
en-wikipedia-org-3337	4	57	at	at	IN
en-wikipedia-org-3337	4	58	maximizing	maximize	VBG
en-wikipedia-org-3337	4	59	his	-PRON-	PRP$
en-wikipedia-org-3337	4	60	payoff	payoff	NN
en-wikipedia-org-3337	4	61	in	in	IN
en-wikipedia-org-3337	4	62	response	response	NN
en-wikipedia-org-3337	4	63	to	to	IN
en-wikipedia-org-3337	4	64	Alice	Alice	NNP
en-wikipedia-org-3337	4	65	choosing	choosing	NN
en-wikipedia-org-3337	4	66	A.	a.	NN
en-wikipedia-org-3337	5	1	In	in	IN
en-wikipedia-org-3337	5	2	a	a	DT
en-wikipedia-org-3337	5	3	game	game	NN
en-wikipedia-org-3337	5	4	in	in	IN
en-wikipedia-org-3337	5	5	which	which	WDT
en-wikipedia-org-3337	5	6	Carol	Carol	NNP
en-wikipedia-org-3337	5	7	and	and	CC
en-wikipedia-org-3337	5	8	Dan	Dan	NNP
en-wikipedia-org-3337	5	9	are	be	VBP
en-wikipedia-org-3337	5	10	also	also	RB
en-wikipedia-org-3337	5	11	players	player	NNS
en-wikipedia-org-3337	5	12	,	,	,
en-wikipedia-org-3337	5	13	(	(	-LRB-
en-wikipedia-org-3337	5	14	A	a	NN
en-wikipedia-org-3337	5	15	,	,	,
en-wikipedia-org-3337	5	16	B	b	NN
en-wikipedia-org-3337	5	17	,	,	,
en-wikipedia-org-3337	5	18	C	C	NNP
en-wikipedia-org-3337	5	19	,	,	,
en-wikipedia-org-3337	5	20	D	D	NNP
en-wikipedia-org-3337	5	21	)	)	-RRB-
en-wikipedia-org-3337	5	22	is	be	VBZ
en-wikipedia-org-3337	5	23	a	a	DT
en-wikipedia-org-3337	5	24	Nash	Nash	NNP
en-wikipedia-org-3337	5	25	equilibrium	equilibrium	NN
en-wikipedia-org-3337	5	26	if	if	IN
en-wikipedia-org-3337	5	27	A	a	DT
en-wikipedia-org-3337	5	28	is	be	VBZ
en-wikipedia-org-3337	5	29	Alice	Alice	NNP
en-wikipedia-org-3337	5	30	's	's	POS
en-wikipedia-org-3337	5	31	best	good	JJS
en-wikipedia-org-3337	5	32	response	response	NN
en-wikipedia-org-3337	5	33	to	to	IN
en-wikipedia-org-3337	5	34	(	(	-LRB-
en-wikipedia-org-3337	5	35	B	b	NN
en-wikipedia-org-3337	5	36	,	,	,
en-wikipedia-org-3337	5	37	C	C	NNP
en-wikipedia-org-3337	5	38	,	,	,
en-wikipedia-org-3337	5	39	D	D	NNP
en-wikipedia-org-3337	5	40	)	)	-RRB-
en-wikipedia-org-3337	5	41	,	,	,
en-wikipedia-org-3337	5	42	B	b	NN
en-wikipedia-org-3337	5	43	is	be	VBZ
en-wikipedia-org-3337	5	44	Bob	Bob	NNP
en-wikipedia-org-3337	5	45	's	's	POS
en-wikipedia-org-3337	5	46	best	good	JJS
en-wikipedia-org-3337	5	47	response	response	NN
en-wikipedia-org-3337	5	48	to	to	IN
en-wikipedia-org-3337	5	49	(	(	-LRB-
en-wikipedia-org-3337	5	50	A	a	NN
en-wikipedia-org-3337	5	51	,	,	,
en-wikipedia-org-3337	5	52	C	c	NN
en-wikipedia-org-3337	5	53	,	,	,
en-wikipedia-org-3337	5	54	D	D	NNP
en-wikipedia-org-3337	5	55	)	)	-RRB-
en-wikipedia-org-3337	5	56	,	,	,
en-wikipedia-org-3337	5	57	and	and	CC
en-wikipedia-org-3337	5	58	so	so	RB
en-wikipedia-org-3337	5	59	forth	forth	RB
en-wikipedia-org-3337	5	60	.	.	.
en-wikipedia-org-3337	6	1	Nash	Nash	NNP
en-wikipedia-org-3337	6	2	showed	show	VBD
en-wikipedia-org-3337	6	3	that	that	IN
en-wikipedia-org-3337	6	4	there	there	EX
en-wikipedia-org-3337	6	5	is	be	VBZ
en-wikipedia-org-3337	6	6	a	a	DT
en-wikipedia-org-3337	6	7	Nash	Nash	NNP
en-wikipedia-org-3337	6	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	6	9	for	for	IN
en-wikipedia-org-3337	6	10	every	every	DT
en-wikipedia-org-3337	6	11	finite	finite	JJ
en-wikipedia-org-3337	6	12	game	game	NN
en-wikipedia-org-3337	6	13	:	:	:
en-wikipedia-org-3337	6	14	see	see	VB
en-wikipedia-org-3337	6	15	further	further	RB
en-wikipedia-org-3337	6	16	the	the	DT
en-wikipedia-org-3337	6	17	article	article	NN
en-wikipedia-org-3337	6	18	on	on	IN
en-wikipedia-org-3337	6	19	strategy	strategy	NN
en-wikipedia-org-3337	6	20	.	.	.
en-wikipedia-org-3337	7	1	Contents	content	NNS
en-wikipedia-org-3337	7	2	1	1	CD
en-wikipedia-org-3337	7	3	Applications	application	NNS
en-wikipedia-org-3337	7	4	2	2	CD
en-wikipedia-org-3337	7	5	History	history	NN
en-wikipedia-org-3337	7	6	3	3	CD
en-wikipedia-org-3337	7	7	Definitions	definition	NNS
en-wikipedia-org-3337	7	8	3.1	3.1	CD
en-wikipedia-org-3337	7	9	Nash	Nash	NNP
en-wikipedia-org-3337	7	10	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	7	11	3.2	3.2	CD
en-wikipedia-org-3337	7	12	Strict	strict	JJ
en-wikipedia-org-3337	7	13	/	/	SYM
en-wikipedia-org-3337	7	14	Weak	Weak	NNP
en-wikipedia-org-3337	7	15	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	7	16	3.3	3.3	CD
en-wikipedia-org-3337	7	17	Nash	Nash	NNP
en-wikipedia-org-3337	7	18	's	's	POS
en-wikipedia-org-3337	7	19	Existence	Existence	NNP
en-wikipedia-org-3337	7	20	Theorem	Theorem	NNP
en-wikipedia-org-3337	7	21	4	4	CD
en-wikipedia-org-3337	7	22	Examples	example	NNS
en-wikipedia-org-3337	7	23	4.1	4.1	CD
en-wikipedia-org-3337	7	24	Coordination	Coordination	NNP
en-wikipedia-org-3337	7	25	game	game	NN
en-wikipedia-org-3337	7	26	4.2	4.2	CD
en-wikipedia-org-3337	7	27	Prisoner	Prisoner	NNP
en-wikipedia-org-3337	7	28	's	's	POS
en-wikipedia-org-3337	7	29	dilemma	dilemma	NN
en-wikipedia-org-3337	7	30	4.3	4.3	CD
en-wikipedia-org-3337	7	31	Network	Network	NNP
en-wikipedia-org-3337	7	32	traffic	traffic	NN
en-wikipedia-org-3337	7	33	4.4	4.4	CD
en-wikipedia-org-3337	7	34	Competition	Competition	NNP
en-wikipedia-org-3337	7	35	game	game	NN
en-wikipedia-org-3337	7	36	4.5	4.5	CD
en-wikipedia-org-3337	7	37	Nash	Nash	NNP
en-wikipedia-org-3337	7	38	equilibria	equilibria	NN
en-wikipedia-org-3337	7	39	in	in	IN
en-wikipedia-org-3337	7	40	a	a	DT
en-wikipedia-org-3337	7	41	payoff	payoff	NN
en-wikipedia-org-3337	7	42	matrix	matrix	NN
en-wikipedia-org-3337	7	43	5	5	CD
en-wikipedia-org-3337	7	44	Stability	Stability	NNP
en-wikipedia-org-3337	7	45	6	6	CD
en-wikipedia-org-3337	7	46	Occurrence	Occurrence	NNP
en-wikipedia-org-3337	7	47	6.1	6.1	CD
en-wikipedia-org-3337	7	48	Where	where	WRB
en-wikipedia-org-3337	7	49	the	the	DT
en-wikipedia-org-3337	7	50	conditions	condition	NNS
en-wikipedia-org-3337	7	51	are	be	VBP
en-wikipedia-org-3337	7	52	not	not	RB
en-wikipedia-org-3337	7	53	met	meet	VBD
en-wikipedia-org-3337	7	54	6.2	6.2	CD
en-wikipedia-org-3337	7	55	Where	where	WRB
en-wikipedia-org-3337	7	56	the	the	DT
en-wikipedia-org-3337	7	57	conditions	condition	NNS
en-wikipedia-org-3337	7	58	are	be	VBP
en-wikipedia-org-3337	7	59	met	meet	VBN
en-wikipedia-org-3337	7	60	7	7	CD
en-wikipedia-org-3337	7	61	NE	NE	NNP
en-wikipedia-org-3337	7	62	and	and	CC
en-wikipedia-org-3337	7	63	non	non	JJ
en-wikipedia-org-3337	7	64	-	-	JJ
en-wikipedia-org-3337	7	65	credible	credible	JJ
en-wikipedia-org-3337	7	66	threats	threat	NNS
en-wikipedia-org-3337	7	67	8	8	CD
en-wikipedia-org-3337	7	68	Proof	proof	NN
en-wikipedia-org-3337	7	69	of	of	IN
en-wikipedia-org-3337	7	70	existence	existence	NN
en-wikipedia-org-3337	7	71	8.1	8.1	CD
en-wikipedia-org-3337	7	72	Proof	Proof	NNP
en-wikipedia-org-3337	7	73	using	use	VBG
en-wikipedia-org-3337	7	74	the	the	DT
en-wikipedia-org-3337	7	75	Kakutani	Kakutani	NNP
en-wikipedia-org-3337	7	76	fixed	fix	VBN
en-wikipedia-org-3337	7	77	-	-	HYPH
en-wikipedia-org-3337	7	78	point	point	NN
en-wikipedia-org-3337	7	79	theorem	theorem	NN
en-wikipedia-org-3337	7	80	8.2	8.2	CD
en-wikipedia-org-3337	7	81	Alternate	alternate	JJ
en-wikipedia-org-3337	7	82	proof	proof	NN
en-wikipedia-org-3337	7	83	using	use	VBG
en-wikipedia-org-3337	7	84	the	the	DT
en-wikipedia-org-3337	7	85	Brouwer	Brouwer	NNP
en-wikipedia-org-3337	7	86	fixed	fix	VBN
en-wikipedia-org-3337	7	87	-	-	HYPH
en-wikipedia-org-3337	7	88	point	point	NN
en-wikipedia-org-3337	7	89	theorem	theorem	NN
en-wikipedia-org-3337	7	90	9	9	CD
en-wikipedia-org-3337	7	91	Computing	Computing	NNP
en-wikipedia-org-3337	7	92	Nash	Nash	NNP
en-wikipedia-org-3337	7	93	equilibria	equilibria	NN
en-wikipedia-org-3337	7	94	9.1	9.1	CD
en-wikipedia-org-3337	7	95	Examples	example	NNS
en-wikipedia-org-3337	7	96	10	10	CD
en-wikipedia-org-3337	7	97	See	see	VBP
en-wikipedia-org-3337	7	98	also	also	RB
en-wikipedia-org-3337	7	99	11	11	CD
en-wikipedia-org-3337	7	100	Notes	note	NNS
en-wikipedia-org-3337	7	101	12	12	CD
en-wikipedia-org-3337	7	102	References	reference	NNS
en-wikipedia-org-3337	7	103	12.1	12.1	CD
en-wikipedia-org-3337	7	104	Game	game	NN
en-wikipedia-org-3337	7	105	theory	theory	NN
en-wikipedia-org-3337	7	106	textbooks	textbook	VBZ
en-wikipedia-org-3337	7	107	12.2	12.2	CD
en-wikipedia-org-3337	7	108	Original	Original	NNP
en-wikipedia-org-3337	7	109	Nash	Nash	NNP
en-wikipedia-org-3337	7	110	papers	paper	NNS
en-wikipedia-org-3337	7	111	12.3	12.3	CD
en-wikipedia-org-3337	7	112	Other	other	JJ
en-wikipedia-org-3337	7	113	references	reference	NNS
en-wikipedia-org-3337	7	114	13	13	CD
en-wikipedia-org-3337	7	115	External	external	JJ
en-wikipedia-org-3337	7	116	links	link	NNS
en-wikipedia-org-3337	7	117	Applications[edit	applications[edit	NN
en-wikipedia-org-3337	7	118	]	]	-RRB-
en-wikipedia-org-3337	7	119	Game	game	NN
en-wikipedia-org-3337	7	120	theorists	theorist	NNS
en-wikipedia-org-3337	7	121	use	use	VBP
en-wikipedia-org-3337	7	122	Nash	Nash	NNP
en-wikipedia-org-3337	7	123	equilibrium	equilibrium	NN
en-wikipedia-org-3337	7	124	to	to	TO
en-wikipedia-org-3337	7	125	analyze	analyze	VB
en-wikipedia-org-3337	7	126	the	the	DT
en-wikipedia-org-3337	7	127	outcome	outcome	NN
en-wikipedia-org-3337	7	128	of	of	IN
en-wikipedia-org-3337	7	129	the	the	DT
en-wikipedia-org-3337	7	130	strategic	strategic	JJ
en-wikipedia-org-3337	7	131	interaction	interaction	NN
en-wikipedia-org-3337	7	132	of	of	IN
en-wikipedia-org-3337	7	133	several	several	JJ
en-wikipedia-org-3337	7	134	decision	decision	NN
en-wikipedia-org-3337	7	135	makers	maker	NNS
en-wikipedia-org-3337	7	136	.	.	.
en-wikipedia-org-3337	8	1	In	in	IN
en-wikipedia-org-3337	8	2	a	a	DT
en-wikipedia-org-3337	8	3	strategic	strategic	JJ
en-wikipedia-org-3337	8	4	interaction	interaction	NN
en-wikipedia-org-3337	8	5	,	,	,
en-wikipedia-org-3337	8	6	the	the	DT
en-wikipedia-org-3337	8	7	outcome	outcome	NN
en-wikipedia-org-3337	8	8	for	for	IN
en-wikipedia-org-3337	8	9	each	each	DT
en-wikipedia-org-3337	8	10	decision	decision	NN
en-wikipedia-org-3337	8	11	-	-	HYPH
en-wikipedia-org-3337	8	12	maker	maker	NN
en-wikipedia-org-3337	8	13	depends	depend	VBZ
en-wikipedia-org-3337	8	14	on	on	IN
en-wikipedia-org-3337	8	15	the	the	DT
en-wikipedia-org-3337	8	16	decisions	decision	NNS
en-wikipedia-org-3337	8	17	of	of	IN
en-wikipedia-org-3337	8	18	the	the	DT
en-wikipedia-org-3337	8	19	others	other	NNS
en-wikipedia-org-3337	8	20	as	as	RB
en-wikipedia-org-3337	8	21	well	well	RB
en-wikipedia-org-3337	8	22	as	as	IN
en-wikipedia-org-3337	8	23	their	-PRON-	PRP$
en-wikipedia-org-3337	8	24	own	own	JJ
en-wikipedia-org-3337	8	25	.	.	.
en-wikipedia-org-3337	9	1	The	the	DT
en-wikipedia-org-3337	9	2	simple	simple	JJ
en-wikipedia-org-3337	9	3	insight	insight	NN
en-wikipedia-org-3337	9	4	underlying	underlie	VBG
en-wikipedia-org-3337	9	5	Nash	Nash	NNP
en-wikipedia-org-3337	9	6	's	's	POS
en-wikipedia-org-3337	9	7	idea	idea	NN
en-wikipedia-org-3337	9	8	is	be	VBZ
en-wikipedia-org-3337	9	9	that	that	IN
en-wikipedia-org-3337	9	10	one	one	PRP
en-wikipedia-org-3337	9	11	can	can	MD
en-wikipedia-org-3337	9	12	not	not	RB
en-wikipedia-org-3337	9	13	predict	predict	VB
en-wikipedia-org-3337	9	14	the	the	DT
en-wikipedia-org-3337	9	15	choices	choice	NNS
en-wikipedia-org-3337	9	16	of	of	IN
en-wikipedia-org-3337	9	17	multiple	multiple	JJ
en-wikipedia-org-3337	9	18	decision	decision	NN
en-wikipedia-org-3337	9	19	makers	maker	NNS
en-wikipedia-org-3337	9	20	if	if	IN
en-wikipedia-org-3337	9	21	one	one	PRP
en-wikipedia-org-3337	9	22	analyzes	analyze	VBZ
en-wikipedia-org-3337	9	23	those	those	DT
en-wikipedia-org-3337	9	24	decisions	decision	NNS
en-wikipedia-org-3337	9	25	in	in	IN
en-wikipedia-org-3337	9	26	isolation	isolation	NN
en-wikipedia-org-3337	9	27	.	.	.
en-wikipedia-org-3337	10	1	Instead	instead	RB
en-wikipedia-org-3337	10	2	,	,	,
en-wikipedia-org-3337	10	3	one	one	PRP
en-wikipedia-org-3337	10	4	must	must	MD
en-wikipedia-org-3337	10	5	ask	ask	VB
en-wikipedia-org-3337	10	6	what	what	WP
en-wikipedia-org-3337	10	7	each	each	DT
en-wikipedia-org-3337	10	8	player	player	NN
en-wikipedia-org-3337	10	9	would	would	MD
en-wikipedia-org-3337	10	10	do	do	VB
en-wikipedia-org-3337	10	11	taking	take	VBG
en-wikipedia-org-3337	10	12	into	into	IN
en-wikipedia-org-3337	10	13	account	account	NN
en-wikipedia-org-3337	10	14	what	what	WP
en-wikipedia-org-3337	10	15	she	-PRON-	PRP
en-wikipedia-org-3337	10	16	/	/	SYM
en-wikipedia-org-3337	10	17	he	-PRON-	PRP
en-wikipedia-org-3337	10	18	expects	expect	VBZ
en-wikipedia-org-3337	10	19	the	the	DT
en-wikipedia-org-3337	10	20	others	other	NNS
en-wikipedia-org-3337	10	21	to	to	TO
en-wikipedia-org-3337	10	22	do	do	VB
en-wikipedia-org-3337	10	23	.	.	.
en-wikipedia-org-3337	11	1	Nash	nash	JJ
en-wikipedia-org-3337	11	2	equilibrium	equilibrium	NN
en-wikipedia-org-3337	11	3	requires	require	VBZ
en-wikipedia-org-3337	11	4	that	that	IN
en-wikipedia-org-3337	11	5	their	-PRON-	PRP$
en-wikipedia-org-3337	11	6	choices	choice	NNS
en-wikipedia-org-3337	11	7	be	be	VB
en-wikipedia-org-3337	11	8	consistent	consistent	JJ
en-wikipedia-org-3337	11	9	:	:	:
en-wikipedia-org-3337	11	10	no	no	DT
en-wikipedia-org-3337	11	11	player	player	NN
en-wikipedia-org-3337	11	12	wishes	wish	VBZ
en-wikipedia-org-3337	11	13	to	to	TO
en-wikipedia-org-3337	11	14	undo	undo	VB
en-wikipedia-org-3337	11	15	their	-PRON-	PRP$
en-wikipedia-org-3337	11	16	decision	decision	NN
en-wikipedia-org-3337	11	17	given	give	VBN
en-wikipedia-org-3337	11	18	what	what	WP
en-wikipedia-org-3337	11	19	the	the	DT
en-wikipedia-org-3337	11	20	others	other	NNS
en-wikipedia-org-3337	11	21	are	be	VBP
en-wikipedia-org-3337	11	22	deciding	decide	VBG
en-wikipedia-org-3337	11	23	.	.	.
en-wikipedia-org-3337	12	1	The	the	DT
en-wikipedia-org-3337	12	2	concept	concept	NN
en-wikipedia-org-3337	12	3	has	have	VBZ
en-wikipedia-org-3337	12	4	been	be	VBN
en-wikipedia-org-3337	12	5	used	use	VBN
en-wikipedia-org-3337	12	6	to	to	TO
en-wikipedia-org-3337	12	7	analyze	analyze	VB
en-wikipedia-org-3337	12	8	hostile	hostile	JJ
en-wikipedia-org-3337	12	9	situations	situation	NNS
en-wikipedia-org-3337	12	10	like	like	IN
en-wikipedia-org-3337	12	11	wars	war	NNS
en-wikipedia-org-3337	12	12	and	and	CC
en-wikipedia-org-3337	12	13	arms	arm	NNS
en-wikipedia-org-3337	12	14	races[3	races[3	NNP
en-wikipedia-org-3337	12	15	]	]	-RRB-
en-wikipedia-org-3337	12	16	(	(	-LRB-
en-wikipedia-org-3337	12	17	see	see	VB
en-wikipedia-org-3337	12	18	prisoner	prisoner	NNP
en-wikipedia-org-3337	12	19	's	's	POS
en-wikipedia-org-3337	12	20	dilemma	dilemma	NN
en-wikipedia-org-3337	12	21	)	)	-RRB-
en-wikipedia-org-3337	12	22	,	,	,
en-wikipedia-org-3337	12	23	and	and	CC
en-wikipedia-org-3337	12	24	also	also	RB
en-wikipedia-org-3337	12	25	how	how	WRB
en-wikipedia-org-3337	12	26	conflict	conflict	NN
en-wikipedia-org-3337	12	27	may	may	MD
en-wikipedia-org-3337	12	28	be	be	VB
en-wikipedia-org-3337	12	29	mitigated	mitigate	VBN
en-wikipedia-org-3337	12	30	by	by	IN
en-wikipedia-org-3337	12	31	repeated	repeat	VBN
en-wikipedia-org-3337	12	32	interaction	interaction	NN
en-wikipedia-org-3337	12	33	(	(	-LRB-
en-wikipedia-org-3337	12	34	see	see	VB
en-wikipedia-org-3337	12	35	tit	tit	NN
en-wikipedia-org-3337	12	36	-	-	HYPH
en-wikipedia-org-3337	12	37	for	for	IN
en-wikipedia-org-3337	12	38	-	-	HYPH
en-wikipedia-org-3337	12	39	tat	tat	NN
en-wikipedia-org-3337	12	40	)	)	-RRB-
en-wikipedia-org-3337	12	41	.	.	.
en-wikipedia-org-3337	13	1	It	-PRON-	PRP
en-wikipedia-org-3337	13	2	has	have	VBZ
en-wikipedia-org-3337	13	3	also	also	RB
en-wikipedia-org-3337	13	4	been	be	VBN
en-wikipedia-org-3337	13	5	used	use	VBN
en-wikipedia-org-3337	13	6	to	to	TO
en-wikipedia-org-3337	13	7	study	study	VB
en-wikipedia-org-3337	13	8	to	to	IN
en-wikipedia-org-3337	13	9	what	what	WDT
en-wikipedia-org-3337	13	10	extent	extent	NN
en-wikipedia-org-3337	13	11	people	people	NNS
en-wikipedia-org-3337	13	12	with	with	IN
en-wikipedia-org-3337	13	13	different	different	JJ
en-wikipedia-org-3337	13	14	preferences	preference	NNS
en-wikipedia-org-3337	13	15	can	can	MD
en-wikipedia-org-3337	13	16	cooperate	cooperate	VB
en-wikipedia-org-3337	13	17	(	(	-LRB-
en-wikipedia-org-3337	13	18	see	see	VB
en-wikipedia-org-3337	13	19	battle	battle	NN
en-wikipedia-org-3337	13	20	of	of	IN
en-wikipedia-org-3337	13	21	the	the	DT
en-wikipedia-org-3337	13	22	sexes	sex	NNS
en-wikipedia-org-3337	13	23	)	)	-RRB-
en-wikipedia-org-3337	13	24	,	,	,
en-wikipedia-org-3337	13	25	and	and	CC
en-wikipedia-org-3337	13	26	whether	whether	IN
en-wikipedia-org-3337	13	27	they	-PRON-	PRP
en-wikipedia-org-3337	13	28	will	will	MD
en-wikipedia-org-3337	13	29	take	take	VB
en-wikipedia-org-3337	13	30	risks	risk	NNS
en-wikipedia-org-3337	13	31	to	to	TO
en-wikipedia-org-3337	13	32	achieve	achieve	VB
en-wikipedia-org-3337	13	33	a	a	DT
en-wikipedia-org-3337	13	34	cooperative	cooperative	JJ
en-wikipedia-org-3337	13	35	outcome	outcome	NN
en-wikipedia-org-3337	13	36	(	(	-LRB-
en-wikipedia-org-3337	13	37	see	see	VB
en-wikipedia-org-3337	13	38	stag	stag	JJ
en-wikipedia-org-3337	13	39	hunt	hunt	NNP
en-wikipedia-org-3337	13	40	)	)	-RRB-
en-wikipedia-org-3337	13	41	.	.	.
en-wikipedia-org-3337	14	1	It	-PRON-	PRP
en-wikipedia-org-3337	14	2	has	have	VBZ
en-wikipedia-org-3337	14	3	been	be	VBN
en-wikipedia-org-3337	14	4	used	use	VBN
en-wikipedia-org-3337	14	5	to	to	TO
en-wikipedia-org-3337	14	6	study	study	VB
en-wikipedia-org-3337	14	7	the	the	DT
en-wikipedia-org-3337	14	8	adoption	adoption	NN
en-wikipedia-org-3337	14	9	of	of	IN
en-wikipedia-org-3337	14	10	technical	technical	JJ
en-wikipedia-org-3337	14	11	standards,[citation	standards,[citation	''
en-wikipedia-org-3337	14	12	needed	need	VBN
en-wikipedia-org-3337	14	13	]	]	-RRB-
en-wikipedia-org-3337	14	14	and	and	CC
en-wikipedia-org-3337	14	15	also	also	RB
en-wikipedia-org-3337	14	16	the	the	DT
en-wikipedia-org-3337	14	17	occurrence	occurrence	NN
en-wikipedia-org-3337	14	18	of	of	IN
en-wikipedia-org-3337	14	19	bank	bank	NN
en-wikipedia-org-3337	14	20	runs	run	NNS
en-wikipedia-org-3337	14	21	and	and	CC
en-wikipedia-org-3337	14	22	currency	currency	NN
en-wikipedia-org-3337	14	23	crises	crisis	NNS
en-wikipedia-org-3337	14	24	(	(	-LRB-
en-wikipedia-org-3337	14	25	see	see	VB
en-wikipedia-org-3337	14	26	coordination	coordination	NN
en-wikipedia-org-3337	14	27	game	game	NN
en-wikipedia-org-3337	14	28	)	)	-RRB-
en-wikipedia-org-3337	14	29	.	.	.
en-wikipedia-org-3337	15	1	Other	other	JJ
en-wikipedia-org-3337	15	2	applications	application	NNS
en-wikipedia-org-3337	15	3	include	include	VBP
en-wikipedia-org-3337	15	4	traffic	traffic	NN
en-wikipedia-org-3337	15	5	flow	flow	NN
en-wikipedia-org-3337	15	6	(	(	-LRB-
en-wikipedia-org-3337	15	7	see	see	VB
en-wikipedia-org-3337	15	8	Wardrop	Wardrop	NNP
en-wikipedia-org-3337	15	9	's	's	POS
en-wikipedia-org-3337	15	10	principle	principle	NN
en-wikipedia-org-3337	15	11	)	)	-RRB-
en-wikipedia-org-3337	15	12	,	,	,
en-wikipedia-org-3337	15	13	how	how	WRB
en-wikipedia-org-3337	15	14	to	to	TO
en-wikipedia-org-3337	15	15	organize	organize	VB
en-wikipedia-org-3337	15	16	auctions	auction	NNS
en-wikipedia-org-3337	15	17	(	(	-LRB-
en-wikipedia-org-3337	15	18	see	see	VB
en-wikipedia-org-3337	15	19	auction	auction	NN
en-wikipedia-org-3337	15	20	theory	theory	NN
en-wikipedia-org-3337	15	21	)	)	-RRB-
en-wikipedia-org-3337	15	22	,	,	,
en-wikipedia-org-3337	15	23	the	the	DT
en-wikipedia-org-3337	15	24	outcome	outcome	NN
en-wikipedia-org-3337	15	25	of	of	IN
en-wikipedia-org-3337	15	26	efforts	effort	NNS
en-wikipedia-org-3337	15	27	exerted	exert	VBN
en-wikipedia-org-3337	15	28	by	by	IN
en-wikipedia-org-3337	15	29	multiple	multiple	JJ
en-wikipedia-org-3337	15	30	parties	party	NNS
en-wikipedia-org-3337	15	31	in	in	IN
en-wikipedia-org-3337	15	32	the	the	DT
en-wikipedia-org-3337	15	33	education	education	NN
en-wikipedia-org-3337	15	34	process,[4	process,[4	NN
en-wikipedia-org-3337	15	35	]	]	-RRB-
en-wikipedia-org-3337	15	36	regulatory	regulatory	JJ
en-wikipedia-org-3337	15	37	legislation	legislation	NN
en-wikipedia-org-3337	15	38	such	such	JJ
en-wikipedia-org-3337	15	39	as	as	IN
en-wikipedia-org-3337	15	40	environmental	environmental	JJ
en-wikipedia-org-3337	15	41	regulations	regulation	NNS
en-wikipedia-org-3337	15	42	(	(	-LRB-
en-wikipedia-org-3337	15	43	see	see	VB
en-wikipedia-org-3337	15	44	tragedy	tragedy	NN
en-wikipedia-org-3337	15	45	of	of	IN
en-wikipedia-org-3337	15	46	the	the	DT
en-wikipedia-org-3337	15	47	commons),[5	commons),[5	JJ
en-wikipedia-org-3337	15	48	]	]	-RRB-
en-wikipedia-org-3337	15	49	natural	natural	JJ
en-wikipedia-org-3337	15	50	resource	resource	NN
en-wikipedia-org-3337	15	51	management,[6	management,[6	NN
en-wikipedia-org-3337	15	52	]	]	-RRB-
en-wikipedia-org-3337	15	53	analysing	analyse	VBG
en-wikipedia-org-3337	15	54	strategies	strategy	NNS
en-wikipedia-org-3337	15	55	in	in	IN
en-wikipedia-org-3337	15	56	marketing,[7	marketing,[7	NNP
en-wikipedia-org-3337	15	57	]	]	-RRB-
en-wikipedia-org-3337	15	58	even	even	RB
en-wikipedia-org-3337	15	59	penalty	penalty	NN
en-wikipedia-org-3337	15	60	kicks	kick	NNS
en-wikipedia-org-3337	15	61	in	in	IN
en-wikipedia-org-3337	15	62	football	football	NN
en-wikipedia-org-3337	15	63	(	(	-LRB-
en-wikipedia-org-3337	15	64	see	see	VB
en-wikipedia-org-3337	15	65	matching	match	VBG
en-wikipedia-org-3337	15	66	pennies),[8	pennies),[8	NN
en-wikipedia-org-3337	15	67	]	]	-RRB-
en-wikipedia-org-3337	15	68	energy	energy	NN
en-wikipedia-org-3337	15	69	systems	system	NNS
en-wikipedia-org-3337	15	70	,	,	,
en-wikipedia-org-3337	15	71	transportation	transportation	NN
en-wikipedia-org-3337	15	72	systems	system	NNS
en-wikipedia-org-3337	15	73	,	,	,
en-wikipedia-org-3337	15	74	evacuation	evacuation	NN
en-wikipedia-org-3337	15	75	problems[9	problems[9	NNP
en-wikipedia-org-3337	15	76	]	]	-RRB-
en-wikipedia-org-3337	15	77	and	and	CC
en-wikipedia-org-3337	15	78	wireless	wireless	JJ
en-wikipedia-org-3337	15	79	communications	communication	NNS
en-wikipedia-org-3337	15	80	.	.	.
en-wikipedia-org-3337	16	1	[	[	-LRB-
en-wikipedia-org-3337	16	2	10	10	CD
en-wikipedia-org-3337	16	3	]	]	-RRB-
en-wikipedia-org-3337	16	4	History[edit	History[edit	VBN
en-wikipedia-org-3337	16	5	]	]	-RRB-
en-wikipedia-org-3337	16	6	Nash	nash	JJ
en-wikipedia-org-3337	16	7	equilibrium	equilibrium	NN
en-wikipedia-org-3337	16	8	is	be	VBZ
en-wikipedia-org-3337	16	9	named	name	VBN
en-wikipedia-org-3337	16	10	after	after	IN
en-wikipedia-org-3337	16	11	American	american	JJ
en-wikipedia-org-3337	16	12	mathematician	mathematician	NN
en-wikipedia-org-3337	16	13	John	John	NNP
en-wikipedia-org-3337	16	14	Forbes	Forbes	NNP
en-wikipedia-org-3337	16	15	Nash	Nash	NNP
en-wikipedia-org-3337	16	16	,	,	,
en-wikipedia-org-3337	16	17	Jr.	Jr.	NNP
en-wikipedia-org-3337	17	1	The	the	DT
en-wikipedia-org-3337	17	2	same	same	JJ
en-wikipedia-org-3337	17	3	idea	idea	NN
en-wikipedia-org-3337	17	4	was	be	VBD
en-wikipedia-org-3337	17	5	used	use	VBN
en-wikipedia-org-3337	17	6	in	in	IN
en-wikipedia-org-3337	17	7	a	a	DT
en-wikipedia-org-3337	17	8	particular	particular	JJ
en-wikipedia-org-3337	17	9	application	application	NN
en-wikipedia-org-3337	17	10	in	in	IN
en-wikipedia-org-3337	17	11	1838	1838	CD
en-wikipedia-org-3337	17	12	by	by	IN
en-wikipedia-org-3337	17	13	Antoine	Antoine	NNP
en-wikipedia-org-3337	17	14	Augustin	Augustin	NNP
en-wikipedia-org-3337	17	15	Cournot	Cournot	NNP
en-wikipedia-org-3337	17	16	in	in	IN
en-wikipedia-org-3337	17	17	his	-PRON-	PRP$
en-wikipedia-org-3337	17	18	theory	theory	NN
en-wikipedia-org-3337	17	19	of	of	IN
en-wikipedia-org-3337	17	20	oligopoly	oligopoly	NN
en-wikipedia-org-3337	17	21	.	.	.
en-wikipedia-org-3337	18	1	[	[	-LRB-
en-wikipedia-org-3337	18	2	11	11	CD
en-wikipedia-org-3337	18	3	]	]	-RRB-
en-wikipedia-org-3337	18	4	In	in	IN
en-wikipedia-org-3337	18	5	Cournot	Cournot	NNP
en-wikipedia-org-3337	18	6	's	's	POS
en-wikipedia-org-3337	18	7	theory	theory	NN
en-wikipedia-org-3337	18	8	,	,	,
en-wikipedia-org-3337	18	9	each	each	DT
en-wikipedia-org-3337	18	10	of	of	IN
en-wikipedia-org-3337	18	11	several	several	JJ
en-wikipedia-org-3337	18	12	firms	firm	NNS
en-wikipedia-org-3337	18	13	choose	choose	VBP
en-wikipedia-org-3337	18	14	how	how	WRB
en-wikipedia-org-3337	18	15	much	much	JJ
en-wikipedia-org-3337	18	16	output	output	NN
en-wikipedia-org-3337	18	17	to	to	TO
en-wikipedia-org-3337	18	18	produce	produce	VB
en-wikipedia-org-3337	18	19	to	to	TO
en-wikipedia-org-3337	18	20	maximize	maximize	VB
en-wikipedia-org-3337	18	21	its	-PRON-	PRP$
en-wikipedia-org-3337	18	22	profit	profit	NN
en-wikipedia-org-3337	18	23	.	.	.
en-wikipedia-org-3337	19	1	The	the	DT
en-wikipedia-org-3337	19	2	best	good	JJS
en-wikipedia-org-3337	19	3	output	output	NN
en-wikipedia-org-3337	19	4	for	for	IN
en-wikipedia-org-3337	19	5	one	one	CD
en-wikipedia-org-3337	19	6	firm	firm	NN
en-wikipedia-org-3337	19	7	depends	depend	VBZ
en-wikipedia-org-3337	19	8	on	on	IN
en-wikipedia-org-3337	19	9	the	the	DT
en-wikipedia-org-3337	19	10	outputs	output	NNS
en-wikipedia-org-3337	19	11	of	of	IN
en-wikipedia-org-3337	19	12	the	the	DT
en-wikipedia-org-3337	19	13	others	other	NNS
en-wikipedia-org-3337	19	14	.	.	.
en-wikipedia-org-3337	20	1	A	a	DT
en-wikipedia-org-3337	20	2	Cournot	Cournot	NNP
en-wikipedia-org-3337	20	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	20	4	occurs	occur	VBZ
en-wikipedia-org-3337	20	5	when	when	WRB
en-wikipedia-org-3337	20	6	each	each	DT
en-wikipedia-org-3337	20	7	firm	firm	NN
en-wikipedia-org-3337	20	8	's	's	POS
en-wikipedia-org-3337	20	9	output	output	NN
en-wikipedia-org-3337	20	10	maximizes	maximize	VBZ
en-wikipedia-org-3337	20	11	its	-PRON-	PRP$
en-wikipedia-org-3337	20	12	profits	profit	NNS
en-wikipedia-org-3337	20	13	given	give	VBN
en-wikipedia-org-3337	20	14	the	the	DT
en-wikipedia-org-3337	20	15	output	output	NN
en-wikipedia-org-3337	20	16	of	of	IN
en-wikipedia-org-3337	20	17	the	the	DT
en-wikipedia-org-3337	20	18	other	other	JJ
en-wikipedia-org-3337	20	19	firms	firm	NNS
en-wikipedia-org-3337	20	20	,	,	,
en-wikipedia-org-3337	20	21	which	which	WDT
en-wikipedia-org-3337	20	22	is	be	VBZ
en-wikipedia-org-3337	20	23	a	a	DT
en-wikipedia-org-3337	20	24	pure	pure	JJ
en-wikipedia-org-3337	20	25	-	-	HYPH
en-wikipedia-org-3337	20	26	strategy	strategy	NN
en-wikipedia-org-3337	20	27	Nash	Nash	NNP
en-wikipedia-org-3337	20	28	equilibrium	equilibrium	NN
en-wikipedia-org-3337	20	29	.	.	.
en-wikipedia-org-3337	21	1	Cournot	Cournot	NNP
en-wikipedia-org-3337	21	2	also	also	RB
en-wikipedia-org-3337	21	3	introduced	introduce	VBD
en-wikipedia-org-3337	21	4	the	the	DT
en-wikipedia-org-3337	21	5	concept	concept	NN
en-wikipedia-org-3337	21	6	of	of	IN
en-wikipedia-org-3337	21	7	best	good	JJS
en-wikipedia-org-3337	21	8	response	response	NN
en-wikipedia-org-3337	21	9	dynamics	dynamic	NNS
en-wikipedia-org-3337	21	10	in	in	IN
en-wikipedia-org-3337	21	11	his	-PRON-	PRP$
en-wikipedia-org-3337	21	12	analysis	analysis	NN
en-wikipedia-org-3337	21	13	of	of	IN
en-wikipedia-org-3337	21	14	the	the	DT
en-wikipedia-org-3337	21	15	stability	stability	NN
en-wikipedia-org-3337	21	16	of	of	IN
en-wikipedia-org-3337	21	17	equilibrium	equilibrium	NN
en-wikipedia-org-3337	21	18	.	.	.
en-wikipedia-org-3337	22	1	Cournot	Cournot	NNP
en-wikipedia-org-3337	22	2	did	do	VBD
en-wikipedia-org-3337	22	3	not	not	RB
en-wikipedia-org-3337	22	4	use	use	VB
en-wikipedia-org-3337	22	5	the	the	DT
en-wikipedia-org-3337	22	6	idea	idea	NN
en-wikipedia-org-3337	22	7	in	in	IN
en-wikipedia-org-3337	22	8	any	any	DT
en-wikipedia-org-3337	22	9	other	other	JJ
en-wikipedia-org-3337	22	10	applications	application	NNS
en-wikipedia-org-3337	22	11	,	,	,
en-wikipedia-org-3337	22	12	however	however	RB
en-wikipedia-org-3337	22	13	,	,	,
en-wikipedia-org-3337	22	14	or	or	CC
en-wikipedia-org-3337	22	15	define	define	VB
en-wikipedia-org-3337	22	16	it	-PRON-	PRP
en-wikipedia-org-3337	22	17	generally	generally	RB
en-wikipedia-org-3337	22	18	.	.	.
en-wikipedia-org-3337	23	1	The	the	DT
en-wikipedia-org-3337	23	2	modern	modern	JJ
en-wikipedia-org-3337	23	3	game	game	NN
en-wikipedia-org-3337	23	4	-	-	HYPH
en-wikipedia-org-3337	23	5	theoretic	theoretic	JJ
en-wikipedia-org-3337	23	6	concept	concept	NN
en-wikipedia-org-3337	23	7	of	of	IN
en-wikipedia-org-3337	23	8	Nash	Nash	NNP
en-wikipedia-org-3337	23	9	equilibrium	equilibrium	NN
en-wikipedia-org-3337	23	10	is	be	VBZ
en-wikipedia-org-3337	23	11	instead	instead	RB
en-wikipedia-org-3337	23	12	defined	define	VBN
en-wikipedia-org-3337	23	13	in	in	IN
en-wikipedia-org-3337	23	14	terms	term	NNS
en-wikipedia-org-3337	23	15	of	of	IN
en-wikipedia-org-3337	23	16	mixed	mixed	JJ
en-wikipedia-org-3337	23	17	strategies	strategy	NNS
en-wikipedia-org-3337	23	18	,	,	,
en-wikipedia-org-3337	23	19	where	where	WRB
en-wikipedia-org-3337	23	20	players	player	NNS
en-wikipedia-org-3337	23	21	choose	choose	VBP
en-wikipedia-org-3337	23	22	a	a	DT
en-wikipedia-org-3337	23	23	probability	probability	NN
en-wikipedia-org-3337	23	24	distribution	distribution	NN
en-wikipedia-org-3337	23	25	over	over	IN
en-wikipedia-org-3337	23	26	possible	possible	JJ
en-wikipedia-org-3337	23	27	actions	action	NNS
en-wikipedia-org-3337	23	28	(	(	-LRB-
en-wikipedia-org-3337	23	29	rather	rather	RB
en-wikipedia-org-3337	23	30	than	than	IN
en-wikipedia-org-3337	23	31	choosing	choose	VBG
en-wikipedia-org-3337	23	32	a	a	DT
en-wikipedia-org-3337	23	33	deterministic	deterministic	JJ
en-wikipedia-org-3337	23	34	action	action	NN
en-wikipedia-org-3337	23	35	to	to	TO
en-wikipedia-org-3337	23	36	be	be	VB
en-wikipedia-org-3337	23	37	played	play	VBN
en-wikipedia-org-3337	23	38	with	with	IN
en-wikipedia-org-3337	23	39	certainty	certainty	NN
en-wikipedia-org-3337	23	40	)	)	-RRB-
en-wikipedia-org-3337	23	41	.	.	.
en-wikipedia-org-3337	24	1	The	the	DT
en-wikipedia-org-3337	24	2	concept	concept	NN
en-wikipedia-org-3337	24	3	of	of	IN
en-wikipedia-org-3337	24	4	a	a	DT
en-wikipedia-org-3337	24	5	mixed	mixed	JJ
en-wikipedia-org-3337	24	6	-	-	HYPH
en-wikipedia-org-3337	24	7	strategy	strategy	NN
en-wikipedia-org-3337	24	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	24	9	was	be	VBD
en-wikipedia-org-3337	24	10	introduced	introduce	VBN
en-wikipedia-org-3337	24	11	by	by	IN
en-wikipedia-org-3337	24	12	John	John	NNP
en-wikipedia-org-3337	24	13	von	von	NNP
en-wikipedia-org-3337	24	14	Neumann	Neumann	NNP
en-wikipedia-org-3337	24	15	and	and	CC
en-wikipedia-org-3337	24	16	Oskar	Oskar	NNP
en-wikipedia-org-3337	24	17	Morgenstern	Morgenstern	NNP
en-wikipedia-org-3337	24	18	in	in	IN
en-wikipedia-org-3337	24	19	their	-PRON-	PRP$
en-wikipedia-org-3337	24	20	1944	1944	CD
en-wikipedia-org-3337	24	21	book	book	NN
en-wikipedia-org-3337	24	22	The	the	DT
en-wikipedia-org-3337	24	23	Theory	Theory	NNP
en-wikipedia-org-3337	24	24	of	of	IN
en-wikipedia-org-3337	24	25	Games	Games	NNPS
en-wikipedia-org-3337	24	26	and	and	CC
en-wikipedia-org-3337	24	27	Economic	Economic	NNP
en-wikipedia-org-3337	24	28	Behavior	Behavior	NNP
en-wikipedia-org-3337	24	29	.	.	.
en-wikipedia-org-3337	25	1	However	however	RB
en-wikipedia-org-3337	25	2	,	,	,
en-wikipedia-org-3337	25	3	their	-PRON-	PRP$
en-wikipedia-org-3337	25	4	analysis	analysis	NN
en-wikipedia-org-3337	25	5	was	be	VBD
en-wikipedia-org-3337	25	6	restricted	restrict	VBN
en-wikipedia-org-3337	25	7	to	to	IN
en-wikipedia-org-3337	25	8	the	the	DT
en-wikipedia-org-3337	25	9	special	special	JJ
en-wikipedia-org-3337	25	10	case	case	NN
en-wikipedia-org-3337	25	11	of	of	IN
en-wikipedia-org-3337	25	12	zero	zero	CD
en-wikipedia-org-3337	25	13	-	-	HYPH
en-wikipedia-org-3337	25	14	sum	sum	NN
en-wikipedia-org-3337	25	15	games	game	NNS
en-wikipedia-org-3337	25	16	.	.	.
en-wikipedia-org-3337	26	1	They	-PRON-	PRP
en-wikipedia-org-3337	26	2	showed	show	VBD
en-wikipedia-org-3337	26	3	that	that	IN
en-wikipedia-org-3337	26	4	a	a	DT
en-wikipedia-org-3337	26	5	mixed	mix	VBN
en-wikipedia-org-3337	26	6	-	-	HYPH
en-wikipedia-org-3337	26	7	strategy	strategy	NN
en-wikipedia-org-3337	26	8	Nash	Nash	NNP
en-wikipedia-org-3337	26	9	equilibrium	equilibrium	NN
en-wikipedia-org-3337	26	10	will	will	MD
en-wikipedia-org-3337	26	11	exist	exist	VB
en-wikipedia-org-3337	26	12	for	for	IN
en-wikipedia-org-3337	26	13	any	any	DT
en-wikipedia-org-3337	26	14	zero	zero	CD
en-wikipedia-org-3337	26	15	-	-	HYPH
en-wikipedia-org-3337	26	16	sum	sum	NN
en-wikipedia-org-3337	26	17	game	game	NN
en-wikipedia-org-3337	26	18	with	with	IN
en-wikipedia-org-3337	26	19	a	a	DT
en-wikipedia-org-3337	26	20	finite	finite	JJ
en-wikipedia-org-3337	26	21	set	set	NN
en-wikipedia-org-3337	26	22	of	of	IN
en-wikipedia-org-3337	26	23	actions	action	NNS
en-wikipedia-org-3337	26	24	.	.	.
en-wikipedia-org-3337	27	1	[	[	-LRB-
en-wikipedia-org-3337	27	2	12	12	CD
en-wikipedia-org-3337	27	3	]	]	-RRB-
en-wikipedia-org-3337	27	4	The	the	DT
en-wikipedia-org-3337	27	5	contribution	contribution	NN
en-wikipedia-org-3337	27	6	of	of	IN
en-wikipedia-org-3337	27	7	Nash	Nash	NNP
en-wikipedia-org-3337	27	8	in	in	IN
en-wikipedia-org-3337	27	9	his	-PRON-	PRP$
en-wikipedia-org-3337	27	10	1951	1951	CD
en-wikipedia-org-3337	27	11	article	article	NN
en-wikipedia-org-3337	27	12	"	"	``
en-wikipedia-org-3337	27	13	Non	non	JJ
en-wikipedia-org-3337	27	14	-	-	JJ
en-wikipedia-org-3337	27	15	Cooperative	Cooperative	NNP
en-wikipedia-org-3337	27	16	Games	Games	NNPS
en-wikipedia-org-3337	27	17	"	"	''
en-wikipedia-org-3337	27	18	was	be	VBD
en-wikipedia-org-3337	27	19	to	to	TO
en-wikipedia-org-3337	27	20	define	define	VB
en-wikipedia-org-3337	27	21	a	a	DT
en-wikipedia-org-3337	27	22	mixed	mix	VBN
en-wikipedia-org-3337	27	23	-	-	HYPH
en-wikipedia-org-3337	27	24	strategy	strategy	NN
en-wikipedia-org-3337	27	25	Nash	Nash	NNP
en-wikipedia-org-3337	27	26	equilibrium	equilibrium	NN
en-wikipedia-org-3337	27	27	for	for	IN
en-wikipedia-org-3337	27	28	any	any	DT
en-wikipedia-org-3337	27	29	game	game	NN
en-wikipedia-org-3337	27	30	with	with	IN
en-wikipedia-org-3337	27	31	a	a	DT
en-wikipedia-org-3337	27	32	finite	finite	JJ
en-wikipedia-org-3337	27	33	set	set	NN
en-wikipedia-org-3337	27	34	of	of	IN
en-wikipedia-org-3337	27	35	actions	action	NNS
en-wikipedia-org-3337	27	36	and	and	CC
en-wikipedia-org-3337	27	37	prove	prove	VB
en-wikipedia-org-3337	27	38	that	that	IN
en-wikipedia-org-3337	27	39	at	at	RB
en-wikipedia-org-3337	27	40	least	least	RBS
en-wikipedia-org-3337	27	41	one	one	CD
en-wikipedia-org-3337	27	42	(	(	-LRB-
en-wikipedia-org-3337	27	43	mixed	mixed	JJ
en-wikipedia-org-3337	27	44	-	-	HYPH
en-wikipedia-org-3337	27	45	strategy	strategy	NN
en-wikipedia-org-3337	27	46	)	)	-RRB-
en-wikipedia-org-3337	27	47	Nash	nash	JJ
en-wikipedia-org-3337	27	48	equilibrium	equilibrium	NN
en-wikipedia-org-3337	27	49	must	must	MD
en-wikipedia-org-3337	27	50	exist	exist	VB
en-wikipedia-org-3337	27	51	in	in	IN
en-wikipedia-org-3337	27	52	such	such	PDT
en-wikipedia-org-3337	27	53	a	a	DT
en-wikipedia-org-3337	27	54	game	game	NN
en-wikipedia-org-3337	27	55	.	.	.
en-wikipedia-org-3337	28	1	The	the	DT
en-wikipedia-org-3337	28	2	key	key	NN
en-wikipedia-org-3337	28	3	to	to	IN
en-wikipedia-org-3337	28	4	Nash	Nash	NNP
en-wikipedia-org-3337	28	5	's	's	POS
en-wikipedia-org-3337	28	6	ability	ability	NN
en-wikipedia-org-3337	28	7	to	to	TO
en-wikipedia-org-3337	28	8	prove	prove	VB
en-wikipedia-org-3337	28	9	existence	existence	NN
en-wikipedia-org-3337	28	10	far	far	RB
en-wikipedia-org-3337	28	11	more	more	RBR
en-wikipedia-org-3337	28	12	generally	generally	RB
en-wikipedia-org-3337	28	13	than	than	IN
en-wikipedia-org-3337	28	14	von	von	NNP
en-wikipedia-org-3337	28	15	Neumann	Neumann	NNP
en-wikipedia-org-3337	28	16	lay	lie	VBD
en-wikipedia-org-3337	28	17	in	in	IN
en-wikipedia-org-3337	28	18	his	-PRON-	PRP$
en-wikipedia-org-3337	28	19	definition	definition	NN
en-wikipedia-org-3337	28	20	of	of	IN
en-wikipedia-org-3337	28	21	equilibrium	equilibrium	NN
en-wikipedia-org-3337	28	22	.	.	.
en-wikipedia-org-3337	29	1	According	accord	VBG
en-wikipedia-org-3337	29	2	to	to	IN
en-wikipedia-org-3337	29	3	Nash	Nash	NNP
en-wikipedia-org-3337	29	4	,	,	,
en-wikipedia-org-3337	29	5	"	"	''
en-wikipedia-org-3337	29	6	an	an	DT
en-wikipedia-org-3337	29	7	equilibrium	equilibrium	NN
en-wikipedia-org-3337	29	8	point	point	NN
en-wikipedia-org-3337	29	9	is	be	VBZ
en-wikipedia-org-3337	29	10	an	an	DT
en-wikipedia-org-3337	29	11	n	n	JJ
en-wikipedia-org-3337	29	12	-	-	HYPH
en-wikipedia-org-3337	29	13	tuple	tuple	NN
en-wikipedia-org-3337	29	14	such	such	JJ
en-wikipedia-org-3337	29	15	that	that	IN
en-wikipedia-org-3337	29	16	each	each	DT
en-wikipedia-org-3337	29	17	player	player	NN
en-wikipedia-org-3337	29	18	's	's	POS
en-wikipedia-org-3337	29	19	mixed	mixed	JJ
en-wikipedia-org-3337	29	20	strategy	strategy	NN
en-wikipedia-org-3337	29	21	maximizes	maximize	VBZ
en-wikipedia-org-3337	29	22	his	-PRON-	PRP$
en-wikipedia-org-3337	29	23	payoff	payoff	NN
en-wikipedia-org-3337	29	24	if	if	IN
en-wikipedia-org-3337	29	25	the	the	DT
en-wikipedia-org-3337	29	26	strategies	strategy	NNS
en-wikipedia-org-3337	29	27	of	of	IN
en-wikipedia-org-3337	29	28	the	the	DT
en-wikipedia-org-3337	29	29	others	other	NNS
en-wikipedia-org-3337	29	30	are	be	VBP
en-wikipedia-org-3337	29	31	held	hold	VBN
en-wikipedia-org-3337	29	32	fixed	fix	VBN
en-wikipedia-org-3337	29	33	.	.	.
en-wikipedia-org-3337	30	1	Thus	thus	RB
en-wikipedia-org-3337	30	2	each	each	DT
en-wikipedia-org-3337	30	3	player	player	NN
en-wikipedia-org-3337	30	4	's	's	POS
en-wikipedia-org-3337	30	5	strategy	strategy	NN
en-wikipedia-org-3337	30	6	is	be	VBZ
en-wikipedia-org-3337	30	7	optimal	optimal	JJ
en-wikipedia-org-3337	30	8	against	against	IN
en-wikipedia-org-3337	30	9	those	those	DT
en-wikipedia-org-3337	30	10	of	of	IN
en-wikipedia-org-3337	30	11	the	the	DT
en-wikipedia-org-3337	30	12	others	other	NNS
en-wikipedia-org-3337	30	13	.	.	.
en-wikipedia-org-3337	30	14	"	"	''
en-wikipedia-org-3337	31	1	Just	just	RB
en-wikipedia-org-3337	31	2	putting	put	VBG
en-wikipedia-org-3337	31	3	the	the	DT
en-wikipedia-org-3337	31	4	problem	problem	NN
en-wikipedia-org-3337	31	5	in	in	IN
en-wikipedia-org-3337	31	6	this	this	DT
en-wikipedia-org-3337	31	7	framework	framework	NN
en-wikipedia-org-3337	31	8	allowed	allow	VBD
en-wikipedia-org-3337	31	9	Nash	Nash	NNP
en-wikipedia-org-3337	31	10	to	to	TO
en-wikipedia-org-3337	31	11	employ	employ	VB
en-wikipedia-org-3337	31	12	the	the	DT
en-wikipedia-org-3337	31	13	Kakutani	Kakutani	NNP
en-wikipedia-org-3337	31	14	fixed	fix	VBN
en-wikipedia-org-3337	31	15	-	-	HYPH
en-wikipedia-org-3337	31	16	point	point	NN
en-wikipedia-org-3337	31	17	theorem	theorem	NN
en-wikipedia-org-3337	31	18	in	in	IN
en-wikipedia-org-3337	31	19	his	-PRON-	PRP$
en-wikipedia-org-3337	31	20	1950	1950	CD
en-wikipedia-org-3337	31	21	paper	paper	NN
en-wikipedia-org-3337	31	22	,	,	,
en-wikipedia-org-3337	31	23	and	and	CC
en-wikipedia-org-3337	31	24	a	a	DT
en-wikipedia-org-3337	31	25	variant	variant	NN
en-wikipedia-org-3337	31	26	upon	upon	IN
en-wikipedia-org-3337	31	27	it	-PRON-	PRP
en-wikipedia-org-3337	31	28	in	in	IN
en-wikipedia-org-3337	31	29	his	-PRON-	PRP$
en-wikipedia-org-3337	31	30	1951	1951	CD
en-wikipedia-org-3337	31	31	paper	paper	NN
en-wikipedia-org-3337	31	32	used	use	VBD
en-wikipedia-org-3337	31	33	the	the	DT
en-wikipedia-org-3337	31	34	Brouwer	Brouwer	NNP
en-wikipedia-org-3337	31	35	fixed	fix	VBN
en-wikipedia-org-3337	31	36	-	-	HYPH
en-wikipedia-org-3337	31	37	point	point	NN
en-wikipedia-org-3337	31	38	theorem	theorem	NN
en-wikipedia-org-3337	31	39	to	to	TO
en-wikipedia-org-3337	31	40	prove	prove	VB
en-wikipedia-org-3337	31	41	that	that	IN
en-wikipedia-org-3337	31	42	there	there	EX
en-wikipedia-org-3337	31	43	had	have	VBD
en-wikipedia-org-3337	31	44	to	to	TO
en-wikipedia-org-3337	31	45	exist	exist	VB
en-wikipedia-org-3337	31	46	at	at	RB
en-wikipedia-org-3337	31	47	least	least	RBS
en-wikipedia-org-3337	31	48	one	one	CD
en-wikipedia-org-3337	31	49	mixed	mix	VBN
en-wikipedia-org-3337	31	50	strategy	strategy	NN
en-wikipedia-org-3337	31	51	profile	profile	NN
en-wikipedia-org-3337	31	52	that	that	WDT
en-wikipedia-org-3337	31	53	mapped	map	VBD
en-wikipedia-org-3337	31	54	back	back	RB
en-wikipedia-org-3337	31	55	into	into	IN
en-wikipedia-org-3337	31	56	itself	-PRON-	PRP
en-wikipedia-org-3337	31	57	for	for	IN
en-wikipedia-org-3337	31	58	finite	finite	NN
en-wikipedia-org-3337	31	59	-	-	HYPH
en-wikipedia-org-3337	31	60	player	player	NN
en-wikipedia-org-3337	31	61	(	(	-LRB-
en-wikipedia-org-3337	31	62	not	not	RB
en-wikipedia-org-3337	31	63	necessarily	necessarily	RB
en-wikipedia-org-3337	31	64	zero	zero	CD
en-wikipedia-org-3337	31	65	-	-	HYPH
en-wikipedia-org-3337	31	66	sum	sum	NN
en-wikipedia-org-3337	31	67	)	)	-RRB-
en-wikipedia-org-3337	31	68	games	game	NNS
en-wikipedia-org-3337	31	69	;	;	:
en-wikipedia-org-3337	31	70	namely	namely	RB
en-wikipedia-org-3337	31	71	,	,	,
en-wikipedia-org-3337	31	72	a	a	DT
en-wikipedia-org-3337	31	73	strategy	strategy	NN
en-wikipedia-org-3337	31	74	profile	profile	NN
en-wikipedia-org-3337	31	75	that	that	WDT
en-wikipedia-org-3337	31	76	did	do	VBD
en-wikipedia-org-3337	31	77	not	not	RB
en-wikipedia-org-3337	31	78	call	call	VB
en-wikipedia-org-3337	31	79	for	for	IN
en-wikipedia-org-3337	31	80	a	a	DT
en-wikipedia-org-3337	31	81	shift	shift	NN
en-wikipedia-org-3337	31	82	in	in	IN
en-wikipedia-org-3337	31	83	strategies	strategy	NNS
en-wikipedia-org-3337	31	84	that	that	WDT
en-wikipedia-org-3337	31	85	could	could	MD
en-wikipedia-org-3337	31	86	improve	improve	VB
en-wikipedia-org-3337	31	87	payoffs	payoff	NNS
en-wikipedia-org-3337	31	88	.	.	.
en-wikipedia-org-3337	32	1	[	[	-LRB-
en-wikipedia-org-3337	32	2	13	13	CD
en-wikipedia-org-3337	32	3	]	]	-RRB-
en-wikipedia-org-3337	32	4	Since	since	IN
en-wikipedia-org-3337	32	5	the	the	DT
en-wikipedia-org-3337	32	6	development	development	NN
en-wikipedia-org-3337	32	7	of	of	IN
en-wikipedia-org-3337	32	8	the	the	DT
en-wikipedia-org-3337	32	9	Nash	Nash	NNP
en-wikipedia-org-3337	32	10	equilibrium	equilibrium	NN
en-wikipedia-org-3337	32	11	concept	concept	NN
en-wikipedia-org-3337	32	12	,	,	,
en-wikipedia-org-3337	32	13	game	game	NN
en-wikipedia-org-3337	32	14	theorists	theorist	NNS
en-wikipedia-org-3337	32	15	have	have	VBP
en-wikipedia-org-3337	32	16	discovered	discover	VBN
en-wikipedia-org-3337	32	17	that	that	IN
en-wikipedia-org-3337	32	18	it	-PRON-	PRP
en-wikipedia-org-3337	32	19	makes	make	VBZ
en-wikipedia-org-3337	32	20	misleading	misleading	JJ
en-wikipedia-org-3337	32	21	predictions	prediction	NNS
en-wikipedia-org-3337	32	22	(	(	-LRB-
en-wikipedia-org-3337	32	23	or	or	CC
en-wikipedia-org-3337	32	24	fails	fail	VBZ
en-wikipedia-org-3337	32	25	to	to	TO
en-wikipedia-org-3337	32	26	make	make	VB
en-wikipedia-org-3337	32	27	a	a	DT
en-wikipedia-org-3337	32	28	unique	unique	JJ
en-wikipedia-org-3337	32	29	prediction	prediction	NN
en-wikipedia-org-3337	32	30	)	)	-RRB-
en-wikipedia-org-3337	32	31	in	in	IN
en-wikipedia-org-3337	32	32	certain	certain	JJ
en-wikipedia-org-3337	32	33	circumstances	circumstance	NNS
en-wikipedia-org-3337	32	34	.	.	.
en-wikipedia-org-3337	33	1	They	-PRON-	PRP
en-wikipedia-org-3337	33	2	have	have	VBP
en-wikipedia-org-3337	33	3	proposed	propose	VBN
en-wikipedia-org-3337	33	4	many	many	JJ
en-wikipedia-org-3337	33	5	related	related	JJ
en-wikipedia-org-3337	33	6	solution	solution	NN
en-wikipedia-org-3337	33	7	concepts	concept	NNS
en-wikipedia-org-3337	33	8	(	(	-LRB-
en-wikipedia-org-3337	33	9	also	also	RB
en-wikipedia-org-3337	33	10	called	call	VBN
en-wikipedia-org-3337	33	11	'	'	``
en-wikipedia-org-3337	33	12	refinements	refinement	NNS
en-wikipedia-org-3337	33	13	'	'	''
en-wikipedia-org-3337	33	14	of	of	IN
en-wikipedia-org-3337	33	15	Nash	Nash	NNP
en-wikipedia-org-3337	33	16	equilibria	equilibria	NN
en-wikipedia-org-3337	33	17	)	)	-RRB-
en-wikipedia-org-3337	33	18	designed	design	VBN
en-wikipedia-org-3337	33	19	to	to	TO
en-wikipedia-org-3337	33	20	overcome	overcome	VB
en-wikipedia-org-3337	33	21	perceived	perceive	VBN
en-wikipedia-org-3337	33	22	flaws	flaw	NNS
en-wikipedia-org-3337	33	23	in	in	IN
en-wikipedia-org-3337	33	24	the	the	DT
en-wikipedia-org-3337	33	25	Nash	Nash	NNP
en-wikipedia-org-3337	33	26	concept	concept	NN
en-wikipedia-org-3337	33	27	.	.	.
en-wikipedia-org-3337	34	1	One	one	CD
en-wikipedia-org-3337	34	2	particularly	particularly	RB
en-wikipedia-org-3337	34	3	important	important	JJ
en-wikipedia-org-3337	34	4	issue	issue	NN
en-wikipedia-org-3337	34	5	is	be	VBZ
en-wikipedia-org-3337	34	6	that	that	IN
en-wikipedia-org-3337	34	7	some	some	DT
en-wikipedia-org-3337	34	8	Nash	Nash	NNP
en-wikipedia-org-3337	34	9	equilibria	equilibria	NN
en-wikipedia-org-3337	34	10	may	may	MD
en-wikipedia-org-3337	34	11	be	be	VB
en-wikipedia-org-3337	34	12	based	base	VBN
en-wikipedia-org-3337	34	13	on	on	IN
en-wikipedia-org-3337	34	14	threats	threat	NNS
en-wikipedia-org-3337	34	15	that	that	WDT
en-wikipedia-org-3337	34	16	are	be	VBP
en-wikipedia-org-3337	34	17	not	not	RB
en-wikipedia-org-3337	34	18	'	'	``
en-wikipedia-org-3337	34	19	credible	credible	JJ
en-wikipedia-org-3337	34	20	'	'	''
en-wikipedia-org-3337	34	21	.	.	.
en-wikipedia-org-3337	35	1	In	in	IN
en-wikipedia-org-3337	35	2	1965	1965	CD
en-wikipedia-org-3337	35	3	Reinhard	Reinhard	NNP
en-wikipedia-org-3337	35	4	Selten	Selten	NNP
en-wikipedia-org-3337	35	5	proposed	propose	VBD
en-wikipedia-org-3337	35	6	subgame	subgame	NN
en-wikipedia-org-3337	35	7	perfect	perfect	JJ
en-wikipedia-org-3337	35	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	35	9	as	as	IN
en-wikipedia-org-3337	35	10	a	a	DT
en-wikipedia-org-3337	35	11	refinement	refinement	NN
en-wikipedia-org-3337	35	12	that	that	WDT
en-wikipedia-org-3337	35	13	eliminates	eliminate	VBZ
en-wikipedia-org-3337	35	14	equilibria	equilibria	NN
en-wikipedia-org-3337	35	15	which	which	WDT
en-wikipedia-org-3337	35	16	depend	depend	VBP
en-wikipedia-org-3337	35	17	on	on	IN
en-wikipedia-org-3337	35	18	non	non	JJ
en-wikipedia-org-3337	35	19	-	-	JJ
en-wikipedia-org-3337	35	20	credible	credible	JJ
en-wikipedia-org-3337	35	21	threats	threat	NNS
en-wikipedia-org-3337	35	22	.	.	.
en-wikipedia-org-3337	36	1	Other	other	JJ
en-wikipedia-org-3337	36	2	extensions	extension	NNS
en-wikipedia-org-3337	36	3	of	of	IN
en-wikipedia-org-3337	36	4	the	the	DT
en-wikipedia-org-3337	36	5	Nash	Nash	NNP
en-wikipedia-org-3337	36	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	36	7	concept	concept	NN
en-wikipedia-org-3337	36	8	have	have	VBP
en-wikipedia-org-3337	36	9	addressed	address	VBN
en-wikipedia-org-3337	36	10	what	what	WP
en-wikipedia-org-3337	36	11	happens	happen	VBZ
en-wikipedia-org-3337	36	12	if	if	IN
en-wikipedia-org-3337	36	13	a	a	DT
en-wikipedia-org-3337	36	14	game	game	NN
en-wikipedia-org-3337	36	15	is	be	VBZ
en-wikipedia-org-3337	36	16	repeated	repeat	VBN
en-wikipedia-org-3337	36	17	,	,	,
en-wikipedia-org-3337	36	18	or	or	CC
en-wikipedia-org-3337	36	19	what	what	WP
en-wikipedia-org-3337	36	20	happens	happen	VBZ
en-wikipedia-org-3337	36	21	if	if	IN
en-wikipedia-org-3337	36	22	a	a	DT
en-wikipedia-org-3337	36	23	game	game	NN
en-wikipedia-org-3337	36	24	is	be	VBZ
en-wikipedia-org-3337	36	25	played	play	VBN
en-wikipedia-org-3337	36	26	in	in	IN
en-wikipedia-org-3337	36	27	the	the	DT
en-wikipedia-org-3337	36	28	absence	absence	NN
en-wikipedia-org-3337	36	29	of	of	IN
en-wikipedia-org-3337	36	30	complete	complete	JJ
en-wikipedia-org-3337	36	31	information	information	NN
en-wikipedia-org-3337	36	32	.	.	.
en-wikipedia-org-3337	37	1	However	however	RB
en-wikipedia-org-3337	37	2	,	,	,
en-wikipedia-org-3337	37	3	subsequent	subsequent	JJ
en-wikipedia-org-3337	37	4	refinements	refinement	NNS
en-wikipedia-org-3337	37	5	and	and	CC
en-wikipedia-org-3337	37	6	extensions	extension	NNS
en-wikipedia-org-3337	37	7	of	of	IN
en-wikipedia-org-3337	37	8	Nash	nash	JJ
en-wikipedia-org-3337	37	9	equilibrium	equilibrium	NN
en-wikipedia-org-3337	37	10	share	share	VBP
en-wikipedia-org-3337	37	11	the	the	DT
en-wikipedia-org-3337	37	12	main	main	JJ
en-wikipedia-org-3337	37	13	insight	insight	NN
en-wikipedia-org-3337	37	14	on	on	IN
en-wikipedia-org-3337	37	15	which	which	WDT
en-wikipedia-org-3337	37	16	Nash	Nash	NNP
en-wikipedia-org-3337	37	17	's	's	POS
en-wikipedia-org-3337	37	18	concept	concept	NN
en-wikipedia-org-3337	37	19	rests	rest	VBZ
en-wikipedia-org-3337	37	20	:	:	:
en-wikipedia-org-3337	37	21	the	the	DT
en-wikipedia-org-3337	37	22	equilibrium	equilibrium	NN
en-wikipedia-org-3337	37	23	is	be	VBZ
en-wikipedia-org-3337	37	24	a	a	DT
en-wikipedia-org-3337	37	25	set	set	NN
en-wikipedia-org-3337	37	26	of	of	IN
en-wikipedia-org-3337	37	27	strategies	strategy	NNS
en-wikipedia-org-3337	37	28	such	such	JJ
en-wikipedia-org-3337	37	29	that	that	IN
en-wikipedia-org-3337	37	30	each	each	DT
en-wikipedia-org-3337	37	31	player	player	NN
en-wikipedia-org-3337	37	32	's	's	POS
en-wikipedia-org-3337	37	33	strategy	strategy	NN
en-wikipedia-org-3337	37	34	is	be	VBZ
en-wikipedia-org-3337	37	35	optimal	optimal	JJ
en-wikipedia-org-3337	37	36	given	give	VBN
en-wikipedia-org-3337	37	37	the	the	DT
en-wikipedia-org-3337	37	38	choices	choice	NNS
en-wikipedia-org-3337	37	39	of	of	IN
en-wikipedia-org-3337	37	40	the	the	DT
en-wikipedia-org-3337	37	41	others	other	NNS
en-wikipedia-org-3337	37	42	.	.	.
en-wikipedia-org-3337	38	1	Definitions[edit	definitions[edit	LS
en-wikipedia-org-3337	38	2	]	]	-RRB-
en-wikipedia-org-3337	38	3	Nash	Nash	NNP
en-wikipedia-org-3337	38	4	Equilibrium[edit	equilibrium[edit	NN
en-wikipedia-org-3337	38	5	]	]	-RRB-
en-wikipedia-org-3337	38	6	Informally	informally	RB
en-wikipedia-org-3337	38	7	,	,	,
en-wikipedia-org-3337	38	8	a	a	DT
en-wikipedia-org-3337	38	9	strategy	strategy	NN
en-wikipedia-org-3337	38	10	profile	profile	NN
en-wikipedia-org-3337	38	11	is	be	VBZ
en-wikipedia-org-3337	38	12	a	a	DT
en-wikipedia-org-3337	38	13	Nash	Nash	NNP
en-wikipedia-org-3337	38	14	equilibrium	equilibrium	NN
en-wikipedia-org-3337	38	15	if	if	IN
en-wikipedia-org-3337	38	16	no	no	DT
en-wikipedia-org-3337	38	17	player	player	NN
en-wikipedia-org-3337	38	18	can	can	MD
en-wikipedia-org-3337	38	19	do	do	VB
en-wikipedia-org-3337	38	20	better	well	RBR
en-wikipedia-org-3337	38	21	by	by	IN
en-wikipedia-org-3337	38	22	unilaterally	unilaterally	RB
en-wikipedia-org-3337	38	23	changing	change	VBG
en-wikipedia-org-3337	38	24	their	-PRON-	PRP$
en-wikipedia-org-3337	38	25	strategy	strategy	NN
en-wikipedia-org-3337	38	26	.	.	.
en-wikipedia-org-3337	39	1	To	to	TO
en-wikipedia-org-3337	39	2	see	see	VB
en-wikipedia-org-3337	39	3	what	what	WP
en-wikipedia-org-3337	39	4	this	this	DT
en-wikipedia-org-3337	39	5	means	mean	VBZ
en-wikipedia-org-3337	39	6	,	,	,
en-wikipedia-org-3337	39	7	imagine	imagine	VBP
en-wikipedia-org-3337	39	8	that	that	IN
en-wikipedia-org-3337	39	9	each	each	DT
en-wikipedia-org-3337	39	10	player	player	NN
en-wikipedia-org-3337	39	11	is	be	VBZ
en-wikipedia-org-3337	39	12	told	tell	VBN
en-wikipedia-org-3337	39	13	the	the	DT
en-wikipedia-org-3337	39	14	strategies	strategy	NNS
en-wikipedia-org-3337	39	15	of	of	IN
en-wikipedia-org-3337	39	16	the	the	DT
en-wikipedia-org-3337	39	17	others	other	NNS
en-wikipedia-org-3337	39	18	.	.	.
en-wikipedia-org-3337	40	1	Suppose	suppose	VB
en-wikipedia-org-3337	40	2	then	then	RB
en-wikipedia-org-3337	40	3	that	that	IN
en-wikipedia-org-3337	40	4	each	each	DT
en-wikipedia-org-3337	40	5	player	player	NN
en-wikipedia-org-3337	40	6	asks	ask	VBZ
en-wikipedia-org-3337	40	7	themselves	-PRON-	PRP
en-wikipedia-org-3337	40	8	:	:	:
en-wikipedia-org-3337	40	9	"	"	``
en-wikipedia-org-3337	40	10	Knowing	know	VBG
en-wikipedia-org-3337	40	11	the	the	DT
en-wikipedia-org-3337	40	12	strategies	strategy	NNS
en-wikipedia-org-3337	40	13	of	of	IN
en-wikipedia-org-3337	40	14	the	the	DT
en-wikipedia-org-3337	40	15	other	other	JJ
en-wikipedia-org-3337	40	16	players	player	NNS
en-wikipedia-org-3337	40	17	,	,	,
en-wikipedia-org-3337	40	18	and	and	CC
en-wikipedia-org-3337	40	19	treating	treat	VBG
en-wikipedia-org-3337	40	20	the	the	DT
en-wikipedia-org-3337	40	21	strategies	strategy	NNS
en-wikipedia-org-3337	40	22	of	of	IN
en-wikipedia-org-3337	40	23	the	the	DT
en-wikipedia-org-3337	40	24	other	other	JJ
en-wikipedia-org-3337	40	25	players	player	NNS
en-wikipedia-org-3337	40	26	as	as	IN
en-wikipedia-org-3337	40	27	set	set	VBN
en-wikipedia-org-3337	40	28	in	in	IN
en-wikipedia-org-3337	40	29	stone	stone	NN
en-wikipedia-org-3337	40	30	,	,	,
en-wikipedia-org-3337	40	31	can	can	MD
en-wikipedia-org-3337	40	32	I	-PRON-	PRP
en-wikipedia-org-3337	40	33	benefit	benefit	VB
en-wikipedia-org-3337	40	34	by	by	IN
en-wikipedia-org-3337	40	35	changing	change	VBG
en-wikipedia-org-3337	40	36	my	-PRON-	PRP$
en-wikipedia-org-3337	40	37	strategy	strategy	NN
en-wikipedia-org-3337	40	38	?	?	.
en-wikipedia-org-3337	40	39	"	"	''
en-wikipedia-org-3337	41	1	If	if	IN
en-wikipedia-org-3337	41	2	any	any	DT
en-wikipedia-org-3337	41	3	player	player	NN
en-wikipedia-org-3337	41	4	could	could	MD
en-wikipedia-org-3337	41	5	answer	answer	VB
en-wikipedia-org-3337	41	6	"	"	``
en-wikipedia-org-3337	41	7	Yes	yes	UH
en-wikipedia-org-3337	41	8	"	"	''
en-wikipedia-org-3337	41	9	,	,	,
en-wikipedia-org-3337	41	10	then	then	RB
en-wikipedia-org-3337	41	11	that	that	DT
en-wikipedia-org-3337	41	12	set	set	NN
en-wikipedia-org-3337	41	13	of	of	IN
en-wikipedia-org-3337	41	14	strategies	strategy	NNS
en-wikipedia-org-3337	41	15	is	be	VBZ
en-wikipedia-org-3337	41	16	not	not	RB
en-wikipedia-org-3337	41	17	a	a	DT
en-wikipedia-org-3337	41	18	Nash	Nash	NNP
en-wikipedia-org-3337	41	19	equilibrium	equilibrium	NN
en-wikipedia-org-3337	41	20	.	.	.
en-wikipedia-org-3337	42	1	But	but	CC
en-wikipedia-org-3337	42	2	if	if	IN
en-wikipedia-org-3337	42	3	every	every	DT
en-wikipedia-org-3337	42	4	player	player	NN
en-wikipedia-org-3337	42	5	prefers	prefer	VBZ
en-wikipedia-org-3337	42	6	not	not	RB
en-wikipedia-org-3337	42	7	to	to	TO
en-wikipedia-org-3337	42	8	switch	switch	VB
en-wikipedia-org-3337	42	9	(	(	-LRB-
en-wikipedia-org-3337	42	10	or	or	CC
en-wikipedia-org-3337	42	11	is	be	VBZ
en-wikipedia-org-3337	42	12	indifferent	indifferent	JJ
en-wikipedia-org-3337	42	13	between	between	IN
en-wikipedia-org-3337	42	14	switching	switch	VBG
en-wikipedia-org-3337	42	15	and	and	CC
en-wikipedia-org-3337	42	16	not	not	RB
en-wikipedia-org-3337	42	17	)	)	-RRB-
en-wikipedia-org-3337	42	18	then	then	RB
en-wikipedia-org-3337	42	19	the	the	DT
en-wikipedia-org-3337	42	20	strategy	strategy	NN
en-wikipedia-org-3337	42	21	profile	profile	NN
en-wikipedia-org-3337	42	22	is	be	VBZ
en-wikipedia-org-3337	42	23	a	a	DT
en-wikipedia-org-3337	42	24	Nash	Nash	NNP
en-wikipedia-org-3337	42	25	equilibrium	equilibrium	NN
en-wikipedia-org-3337	42	26	.	.	.
en-wikipedia-org-3337	43	1	Thus	thus	RB
en-wikipedia-org-3337	43	2	,	,	,
en-wikipedia-org-3337	43	3	each	each	DT
en-wikipedia-org-3337	43	4	strategy	strategy	NN
en-wikipedia-org-3337	43	5	in	in	IN
en-wikipedia-org-3337	43	6	a	a	DT
en-wikipedia-org-3337	43	7	Nash	Nash	NNP
en-wikipedia-org-3337	43	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	43	9	is	be	VBZ
en-wikipedia-org-3337	43	10	a	a	DT
en-wikipedia-org-3337	43	11	best	good	JJS
en-wikipedia-org-3337	43	12	response	response	NN
en-wikipedia-org-3337	43	13	to	to	IN
en-wikipedia-org-3337	43	14	all	all	DT
en-wikipedia-org-3337	43	15	other	other	JJ
en-wikipedia-org-3337	43	16	strategies	strategy	NNS
en-wikipedia-org-3337	43	17	in	in	IN
en-wikipedia-org-3337	43	18	that	that	DT
en-wikipedia-org-3337	43	19	equilibrium	equilibrium	NN
en-wikipedia-org-3337	43	20	.	.	.
en-wikipedia-org-3337	44	1	[	[	-LRB-
en-wikipedia-org-3337	44	2	14	14	CD
en-wikipedia-org-3337	44	3	]	]	-RRB-
en-wikipedia-org-3337	44	4	The	the	DT
en-wikipedia-org-3337	44	5	Nash	Nash	NNP
en-wikipedia-org-3337	44	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	44	7	may	may	MD
en-wikipedia-org-3337	44	8	sometimes	sometimes	RB
en-wikipedia-org-3337	44	9	appear	appear	VB
en-wikipedia-org-3337	44	10	non	non	JJ
en-wikipedia-org-3337	44	11	-	-	JJ
en-wikipedia-org-3337	44	12	rational	rational	JJ
en-wikipedia-org-3337	44	13	in	in	IN
en-wikipedia-org-3337	44	14	a	a	DT
en-wikipedia-org-3337	44	15	third	third	JJ
en-wikipedia-org-3337	44	16	-	-	HYPH
en-wikipedia-org-3337	44	17	person	person	NN
en-wikipedia-org-3337	44	18	perspective	perspective	NN
en-wikipedia-org-3337	44	19	.	.	.
en-wikipedia-org-3337	45	1	This	this	DT
en-wikipedia-org-3337	45	2	is	be	VBZ
en-wikipedia-org-3337	45	3	because	because	IN
en-wikipedia-org-3337	45	4	a	a	DT
en-wikipedia-org-3337	45	5	Nash	Nash	NNP
en-wikipedia-org-3337	45	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	45	7	is	be	VBZ
en-wikipedia-org-3337	45	8	not	not	RB
en-wikipedia-org-3337	45	9	necessarily	necessarily	RB
en-wikipedia-org-3337	45	10	Pareto	Pareto	NNP
en-wikipedia-org-3337	45	11	optimal	optimal	NNP
en-wikipedia-org-3337	45	12	.	.	.
en-wikipedia-org-3337	46	1	The	the	DT
en-wikipedia-org-3337	46	2	Nash	Nash	NNP
en-wikipedia-org-3337	46	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	46	4	may	may	MD
en-wikipedia-org-3337	46	5	also	also	RB
en-wikipedia-org-3337	46	6	have	have	VB
en-wikipedia-org-3337	46	7	non	non	JJ
en-wikipedia-org-3337	46	8	-	-	JJ
en-wikipedia-org-3337	46	9	rational	rational	JJ
en-wikipedia-org-3337	46	10	consequences	consequence	NNS
en-wikipedia-org-3337	46	11	in	in	IN
en-wikipedia-org-3337	46	12	sequential	sequential	JJ
en-wikipedia-org-3337	46	13	games	game	NNS
en-wikipedia-org-3337	46	14	because	because	IN
en-wikipedia-org-3337	46	15	players	player	NNS
en-wikipedia-org-3337	46	16	may	may	MD
en-wikipedia-org-3337	46	17	"	"	``
en-wikipedia-org-3337	46	18	threaten	threaten	VB
en-wikipedia-org-3337	46	19	"	"	''
en-wikipedia-org-3337	46	20	each	each	DT
en-wikipedia-org-3337	46	21	other	other	JJ
en-wikipedia-org-3337	46	22	with	with	IN
en-wikipedia-org-3337	46	23	non	non	JJ
en-wikipedia-org-3337	46	24	-	-	JJ
en-wikipedia-org-3337	46	25	rational	rational	JJ
en-wikipedia-org-3337	46	26	moves	move	NNS
en-wikipedia-org-3337	46	27	.	.	.
en-wikipedia-org-3337	47	1	For	for	IN
en-wikipedia-org-3337	47	2	such	such	JJ
en-wikipedia-org-3337	47	3	games	game	NNS
en-wikipedia-org-3337	47	4	the	the	DT
en-wikipedia-org-3337	47	5	subgame	subgame	NN
en-wikipedia-org-3337	47	6	perfect	perfect	JJ
en-wikipedia-org-3337	47	7	Nash	Nash	NNP
en-wikipedia-org-3337	47	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	47	9	may	may	MD
en-wikipedia-org-3337	47	10	be	be	VB
en-wikipedia-org-3337	47	11	more	more	RBR
en-wikipedia-org-3337	47	12	meaningful	meaningful	JJ
en-wikipedia-org-3337	47	13	as	as	IN
en-wikipedia-org-3337	47	14	a	a	DT
en-wikipedia-org-3337	47	15	tool	tool	NN
en-wikipedia-org-3337	47	16	of	of	IN
en-wikipedia-org-3337	47	17	analysis	analysis	NN
en-wikipedia-org-3337	47	18	.	.	.
en-wikipedia-org-3337	48	1	Strict	strict	JJ
en-wikipedia-org-3337	48	2	/	/	SYM
en-wikipedia-org-3337	48	3	Weak	weak	JJ
en-wikipedia-org-3337	48	4	Equilibrium[edit	equilibrium[edit	NN
en-wikipedia-org-3337	48	5	]	]	-RRB-
en-wikipedia-org-3337	48	6	Suppose	suppose	VB
en-wikipedia-org-3337	48	7	that	that	IN
en-wikipedia-org-3337	48	8	in	in	IN
en-wikipedia-org-3337	48	9	the	the	DT
en-wikipedia-org-3337	48	10	Nash	Nash	NNP
en-wikipedia-org-3337	48	11	equilibrium	equilibrium	NN
en-wikipedia-org-3337	48	12	,	,	,
en-wikipedia-org-3337	48	13	each	each	DT
en-wikipedia-org-3337	48	14	player	player	NN
en-wikipedia-org-3337	48	15	asks	ask	VBZ
en-wikipedia-org-3337	48	16	themselves	-PRON-	PRP
en-wikipedia-org-3337	48	17	:	:	:
en-wikipedia-org-3337	48	18	"	"	``
en-wikipedia-org-3337	48	19	Knowing	know	VBG
en-wikipedia-org-3337	48	20	the	the	DT
en-wikipedia-org-3337	48	21	strategies	strategy	NNS
en-wikipedia-org-3337	48	22	of	of	IN
en-wikipedia-org-3337	48	23	the	the	DT
en-wikipedia-org-3337	48	24	other	other	JJ
en-wikipedia-org-3337	48	25	players	player	NNS
en-wikipedia-org-3337	48	26	,	,	,
en-wikipedia-org-3337	48	27	and	and	CC
en-wikipedia-org-3337	48	28	treating	treat	VBG
en-wikipedia-org-3337	48	29	the	the	DT
en-wikipedia-org-3337	48	30	strategies	strategy	NNS
en-wikipedia-org-3337	48	31	of	of	IN
en-wikipedia-org-3337	48	32	the	the	DT
en-wikipedia-org-3337	48	33	other	other	JJ
en-wikipedia-org-3337	48	34	players	player	NNS
en-wikipedia-org-3337	48	35	as	as	IN
en-wikipedia-org-3337	48	36	set	set	VBN
en-wikipedia-org-3337	48	37	in	in	IN
en-wikipedia-org-3337	48	38	stone	stone	NN
en-wikipedia-org-3337	48	39	,	,	,
en-wikipedia-org-3337	48	40	would	would	MD
en-wikipedia-org-3337	48	41	I	-PRON-	PRP
en-wikipedia-org-3337	48	42	suffer	suffer	VB
en-wikipedia-org-3337	48	43	a	a	DT
en-wikipedia-org-3337	48	44	loss	loss	NN
en-wikipedia-org-3337	48	45	by	by	IN
en-wikipedia-org-3337	48	46	changing	change	VBG
en-wikipedia-org-3337	48	47	my	-PRON-	PRP$
en-wikipedia-org-3337	48	48	strategy	strategy	NN
en-wikipedia-org-3337	48	49	?	?	.
en-wikipedia-org-3337	48	50	"	"	''
en-wikipedia-org-3337	49	1	If	if	IN
en-wikipedia-org-3337	49	2	every	every	DT
en-wikipedia-org-3337	49	3	player	player	NN
en-wikipedia-org-3337	49	4	's	's	POS
en-wikipedia-org-3337	49	5	answer	answer	NN
en-wikipedia-org-3337	49	6	is	be	VBZ
en-wikipedia-org-3337	49	7	"	"	``
en-wikipedia-org-3337	49	8	Yes	yes	UH
en-wikipedia-org-3337	49	9	"	"	''
en-wikipedia-org-3337	49	10	,	,	,
en-wikipedia-org-3337	49	11	then	then	RB
en-wikipedia-org-3337	49	12	the	the	DT
en-wikipedia-org-3337	49	13	equilibrium	equilibrium	NN
en-wikipedia-org-3337	49	14	is	be	VBZ
en-wikipedia-org-3337	49	15	classified	classify	VBN
en-wikipedia-org-3337	49	16	as	as	IN
en-wikipedia-org-3337	49	17	a	a	DT
en-wikipedia-org-3337	49	18	strict	strict	JJ
en-wikipedia-org-3337	49	19	Nash	Nash	NNP
en-wikipedia-org-3337	49	20	equilibrium	equilibrium	NN
en-wikipedia-org-3337	49	21	.	.	.
en-wikipedia-org-3337	50	1	[	[	-LRB-
en-wikipedia-org-3337	50	2	15	15	CD
en-wikipedia-org-3337	50	3	]	]	-RRB-
en-wikipedia-org-3337	50	4	If	if	IN
en-wikipedia-org-3337	50	5	instead	instead	RB
en-wikipedia-org-3337	50	6	,	,	,
en-wikipedia-org-3337	50	7	for	for	IN
en-wikipedia-org-3337	50	8	some	some	DT
en-wikipedia-org-3337	50	9	player	player	NN
en-wikipedia-org-3337	50	10	,	,	,
en-wikipedia-org-3337	50	11	there	there	EX
en-wikipedia-org-3337	50	12	is	be	VBZ
en-wikipedia-org-3337	50	13	exact	exact	JJ
en-wikipedia-org-3337	50	14	equality	equality	NN
en-wikipedia-org-3337	50	15	between	between	IN
en-wikipedia-org-3337	50	16	the	the	DT
en-wikipedia-org-3337	50	17	strategy	strategy	NN
en-wikipedia-org-3337	50	18	in	in	IN
en-wikipedia-org-3337	50	19	Nash	Nash	NNP
en-wikipedia-org-3337	50	20	equilibrium	equilibrium	NN
en-wikipedia-org-3337	50	21	and	and	CC
en-wikipedia-org-3337	50	22	some	some	DT
en-wikipedia-org-3337	50	23	other	other	JJ
en-wikipedia-org-3337	50	24	strategy	strategy	NN
en-wikipedia-org-3337	50	25	that	that	WDT
en-wikipedia-org-3337	50	26	gives	give	VBZ
en-wikipedia-org-3337	50	27	exactly	exactly	RB
en-wikipedia-org-3337	50	28	the	the	DT
en-wikipedia-org-3337	50	29	same	same	JJ
en-wikipedia-org-3337	50	30	payout	payout	NN
en-wikipedia-org-3337	50	31	(	(	-LRB-
en-wikipedia-org-3337	50	32	i.e.	i.e.	FW
en-wikipedia-org-3337	51	1	this	this	DT
en-wikipedia-org-3337	51	2	player	player	NN
en-wikipedia-org-3337	51	3	is	be	VBZ
en-wikipedia-org-3337	51	4	indifferent	indifferent	JJ
en-wikipedia-org-3337	51	5	between	between	IN
en-wikipedia-org-3337	51	6	switching	switch	VBG
en-wikipedia-org-3337	51	7	and	and	CC
en-wikipedia-org-3337	51	8	not	not	RB
en-wikipedia-org-3337	51	9	)	)	-RRB-
en-wikipedia-org-3337	51	10	,	,	,
en-wikipedia-org-3337	51	11	then	then	RB
en-wikipedia-org-3337	51	12	the	the	DT
en-wikipedia-org-3337	51	13	equilibrium	equilibrium	NN
en-wikipedia-org-3337	51	14	is	be	VBZ
en-wikipedia-org-3337	51	15	classified	classify	VBN
en-wikipedia-org-3337	51	16	as	as	IN
en-wikipedia-org-3337	51	17	a	a	DT
en-wikipedia-org-3337	51	18	weak	weak	JJ
en-wikipedia-org-3337	51	19	Nash	Nash	NNP
en-wikipedia-org-3337	51	20	equilibrium	equilibrium	NN
en-wikipedia-org-3337	51	21	.	.	.
en-wikipedia-org-3337	52	1	A	a	DT
en-wikipedia-org-3337	52	2	game	game	NN
en-wikipedia-org-3337	52	3	can	can	MD
en-wikipedia-org-3337	52	4	have	have	VB
en-wikipedia-org-3337	52	5	a	a	DT
en-wikipedia-org-3337	52	6	pure	pure	JJ
en-wikipedia-org-3337	52	7	-	-	HYPH
en-wikipedia-org-3337	52	8	strategy	strategy	NN
en-wikipedia-org-3337	52	9	or	or	CC
en-wikipedia-org-3337	52	10	a	a	DT
en-wikipedia-org-3337	52	11	mixed	mix	VBN
en-wikipedia-org-3337	52	12	-	-	HYPH
en-wikipedia-org-3337	52	13	strategy	strategy	NN
en-wikipedia-org-3337	52	14	Nash	Nash	NNP
en-wikipedia-org-3337	52	15	equilibrium	equilibrium	NN
en-wikipedia-org-3337	52	16	.	.	.
en-wikipedia-org-3337	53	1	(	(	-LRB-
en-wikipedia-org-3337	53	2	In	in	IN
en-wikipedia-org-3337	53	3	the	the	DT
en-wikipedia-org-3337	53	4	latter	latter	JJ
en-wikipedia-org-3337	53	5	a	a	DT
en-wikipedia-org-3337	53	6	pure	pure	JJ
en-wikipedia-org-3337	53	7	strategy	strategy	NN
en-wikipedia-org-3337	53	8	is	be	VBZ
en-wikipedia-org-3337	53	9	chosen	choose	VBN
en-wikipedia-org-3337	53	10	stochastically	stochastically	RB
en-wikipedia-org-3337	53	11	with	with	IN
en-wikipedia-org-3337	53	12	a	a	DT
en-wikipedia-org-3337	53	13	fixed	fix	VBN
en-wikipedia-org-3337	53	14	probability	probability	NN
en-wikipedia-org-3337	53	15	)	)	-RRB-
en-wikipedia-org-3337	53	16	.	.	.
en-wikipedia-org-3337	54	1	Nash	Nash	NNP
en-wikipedia-org-3337	54	2	's	's	POS
en-wikipedia-org-3337	54	3	Existence	Existence	NNP
en-wikipedia-org-3337	54	4	Theorem[edit	Theorem[edit	''
en-wikipedia-org-3337	54	5	]	]	-RRB-
en-wikipedia-org-3337	54	6	Nash	Nash	NNP
en-wikipedia-org-3337	54	7	proved	prove	VBD
en-wikipedia-org-3337	54	8	that	that	IN
en-wikipedia-org-3337	54	9	if	if	IN
en-wikipedia-org-3337	54	10	mixed	mixed	JJ
en-wikipedia-org-3337	54	11	strategies	strategy	NNS
en-wikipedia-org-3337	54	12	(	(	-LRB-
en-wikipedia-org-3337	54	13	where	where	WRB
en-wikipedia-org-3337	54	14	a	a	DT
en-wikipedia-org-3337	54	15	player	player	NN
en-wikipedia-org-3337	54	16	chooses	choose	VBZ
en-wikipedia-org-3337	54	17	probabilities	probability	NNS
en-wikipedia-org-3337	54	18	of	of	IN
en-wikipedia-org-3337	54	19	using	use	VBG
en-wikipedia-org-3337	54	20	various	various	JJ
en-wikipedia-org-3337	54	21	pure	pure	JJ
en-wikipedia-org-3337	54	22	strategies	strategy	NNS
en-wikipedia-org-3337	54	23	)	)	-RRB-
en-wikipedia-org-3337	54	24	are	be	VBP
en-wikipedia-org-3337	54	25	allowed	allow	VBN
en-wikipedia-org-3337	54	26	,	,	,
en-wikipedia-org-3337	54	27	then	then	RB
en-wikipedia-org-3337	54	28	every	every	DT
en-wikipedia-org-3337	54	29	game	game	NN
en-wikipedia-org-3337	54	30	with	with	IN
en-wikipedia-org-3337	54	31	a	a	DT
en-wikipedia-org-3337	54	32	finite	finite	JJ
en-wikipedia-org-3337	54	33	number	number	NN
en-wikipedia-org-3337	54	34	of	of	IN
en-wikipedia-org-3337	54	35	players	player	NNS
en-wikipedia-org-3337	54	36	in	in	IN
en-wikipedia-org-3337	54	37	which	which	WDT
en-wikipedia-org-3337	54	38	each	each	DT
en-wikipedia-org-3337	54	39	player	player	NN
en-wikipedia-org-3337	54	40	can	can	MD
en-wikipedia-org-3337	54	41	choose	choose	VB
en-wikipedia-org-3337	54	42	from	from	IN
en-wikipedia-org-3337	54	43	finitely	finitely	RB
en-wikipedia-org-3337	54	44	many	many	JJ
en-wikipedia-org-3337	54	45	pure	pure	JJ
en-wikipedia-org-3337	54	46	strategies	strategy	NNS
en-wikipedia-org-3337	54	47	has	have	VBZ
en-wikipedia-org-3337	54	48	at	at	RB
en-wikipedia-org-3337	54	49	least	least	RBS
en-wikipedia-org-3337	54	50	one	one	CD
en-wikipedia-org-3337	54	51	Nash	Nash	NNP
en-wikipedia-org-3337	54	52	equilibrium	equilibrium	NN
en-wikipedia-org-3337	54	53	,	,	,
en-wikipedia-org-3337	54	54	which	which	WDT
en-wikipedia-org-3337	54	55	might	may	MD
en-wikipedia-org-3337	54	56	be	be	VB
en-wikipedia-org-3337	54	57	a	a	DT
en-wikipedia-org-3337	54	58	pure	pure	JJ
en-wikipedia-org-3337	54	59	strategy	strategy	NN
en-wikipedia-org-3337	54	60	for	for	IN
en-wikipedia-org-3337	54	61	each	each	DT
en-wikipedia-org-3337	54	62	player	player	NN
en-wikipedia-org-3337	54	63	or	or	CC
en-wikipedia-org-3337	54	64	might	may	MD
en-wikipedia-org-3337	54	65	be	be	VB
en-wikipedia-org-3337	54	66	a	a	DT
en-wikipedia-org-3337	54	67	probability	probability	NN
en-wikipedia-org-3337	54	68	distribution	distribution	NN
en-wikipedia-org-3337	54	69	over	over	IN
en-wikipedia-org-3337	54	70	strategies	strategy	NNS
en-wikipedia-org-3337	54	71	for	for	IN
en-wikipedia-org-3337	54	72	each	each	DT
en-wikipedia-org-3337	54	73	player	player	NN
en-wikipedia-org-3337	54	74	.	.	.
en-wikipedia-org-3337	55	1	Nash	nash	JJ
en-wikipedia-org-3337	55	2	equilibria	equilibria	NN
en-wikipedia-org-3337	55	3	need	need	VBP
en-wikipedia-org-3337	55	4	not	not	RB
en-wikipedia-org-3337	55	5	exist	exist	VB
en-wikipedia-org-3337	55	6	if	if	IN
en-wikipedia-org-3337	55	7	the	the	DT
en-wikipedia-org-3337	55	8	set	set	NN
en-wikipedia-org-3337	55	9	of	of	IN
en-wikipedia-org-3337	55	10	choices	choice	NNS
en-wikipedia-org-3337	55	11	is	be	VBZ
en-wikipedia-org-3337	55	12	infinite	infinite	JJ
en-wikipedia-org-3337	55	13	and	and	CC
en-wikipedia-org-3337	55	14	non	non	JJ
en-wikipedia-org-3337	55	15	-	-	JJ
en-wikipedia-org-3337	55	16	compact	compact	JJ
en-wikipedia-org-3337	55	17	.	.	.
en-wikipedia-org-3337	56	1	An	an	DT
en-wikipedia-org-3337	56	2	example	example	NN
en-wikipedia-org-3337	56	3	is	be	VBZ
en-wikipedia-org-3337	56	4	a	a	DT
en-wikipedia-org-3337	56	5	game	game	NN
en-wikipedia-org-3337	56	6	where	where	WRB
en-wikipedia-org-3337	56	7	two	two	CD
en-wikipedia-org-3337	56	8	players	player	NNS
en-wikipedia-org-3337	56	9	simultaneously	simultaneously	RB
en-wikipedia-org-3337	56	10	name	name	VBP
en-wikipedia-org-3337	56	11	a	a	DT
en-wikipedia-org-3337	56	12	number	number	NN
en-wikipedia-org-3337	56	13	and	and	CC
en-wikipedia-org-3337	56	14	the	the	DT
en-wikipedia-org-3337	56	15	player	player	NN
en-wikipedia-org-3337	56	16	naming	name	VBG
en-wikipedia-org-3337	56	17	the	the	DT
en-wikipedia-org-3337	56	18	larger	large	JJR
en-wikipedia-org-3337	56	19	number	number	NN
en-wikipedia-org-3337	56	20	wins	win	VBZ
en-wikipedia-org-3337	56	21	.	.	.
en-wikipedia-org-3337	57	1	Another	another	DT
en-wikipedia-org-3337	57	2	example	example	NN
en-wikipedia-org-3337	57	3	is	be	VBZ
en-wikipedia-org-3337	57	4	where	where	WRB
en-wikipedia-org-3337	57	5	each	each	DT
en-wikipedia-org-3337	57	6	of	of	IN
en-wikipedia-org-3337	57	7	two	two	CD
en-wikipedia-org-3337	57	8	players	player	NNS
en-wikipedia-org-3337	57	9	chooses	choose	VBZ
en-wikipedia-org-3337	57	10	a	a	DT
en-wikipedia-org-3337	57	11	real	real	JJ
en-wikipedia-org-3337	57	12	number	number	NN
en-wikipedia-org-3337	57	13	strictly	strictly	RB
en-wikipedia-org-3337	57	14	less	less	JJR
en-wikipedia-org-3337	57	15	than	than	IN
en-wikipedia-org-3337	57	16	5	5	CD
en-wikipedia-org-3337	57	17	and	and	CC
en-wikipedia-org-3337	57	18	the	the	DT
en-wikipedia-org-3337	57	19	winner	winner	NN
en-wikipedia-org-3337	57	20	is	be	VBZ
en-wikipedia-org-3337	57	21	whoever	whoever	WP
en-wikipedia-org-3337	57	22	has	have	VBZ
en-wikipedia-org-3337	57	23	the	the	DT
en-wikipedia-org-3337	57	24	biggest	big	JJS
en-wikipedia-org-3337	57	25	number	number	NN
en-wikipedia-org-3337	57	26	;	;	:
en-wikipedia-org-3337	57	27	no	no	DT
en-wikipedia-org-3337	57	28	biggest	big	JJS
en-wikipedia-org-3337	57	29	number	number	NN
en-wikipedia-org-3337	57	30	strictly	strictly	RB
en-wikipedia-org-3337	57	31	less	less	JJR
en-wikipedia-org-3337	57	32	than	than	IN
en-wikipedia-org-3337	57	33	5	5	CD
en-wikipedia-org-3337	57	34	exists	exist	NNS
en-wikipedia-org-3337	57	35	(	(	-LRB-
en-wikipedia-org-3337	57	36	if	if	IN
en-wikipedia-org-3337	57	37	the	the	DT
en-wikipedia-org-3337	57	38	number	number	NN
en-wikipedia-org-3337	57	39	could	could	MD
en-wikipedia-org-3337	57	40	equal	equal	VB
en-wikipedia-org-3337	57	41	5	5	CD
en-wikipedia-org-3337	57	42	,	,	,
en-wikipedia-org-3337	57	43	the	the	DT
en-wikipedia-org-3337	57	44	Nash	Nash	NNP
en-wikipedia-org-3337	57	45	equilibrium	equilibrium	NN
en-wikipedia-org-3337	57	46	would	would	MD
en-wikipedia-org-3337	57	47	have	have	VB
en-wikipedia-org-3337	57	48	both	both	DT
en-wikipedia-org-3337	57	49	players	player	NNS
en-wikipedia-org-3337	57	50	choosing	choose	VBG
en-wikipedia-org-3337	57	51	5	5	CD
en-wikipedia-org-3337	57	52	and	and	CC
en-wikipedia-org-3337	57	53	tying	tie	VBG
en-wikipedia-org-3337	57	54	the	the	DT
en-wikipedia-org-3337	57	55	game	game	NN
en-wikipedia-org-3337	57	56	)	)	-RRB-
en-wikipedia-org-3337	57	57	.	.	.
en-wikipedia-org-3337	58	1	However	however	RB
en-wikipedia-org-3337	58	2	,	,	,
en-wikipedia-org-3337	58	3	a	a	DT
en-wikipedia-org-3337	58	4	Nash	Nash	NNP
en-wikipedia-org-3337	58	5	equilibrium	equilibrium	NN
en-wikipedia-org-3337	58	6	exists	exist	VBZ
en-wikipedia-org-3337	58	7	if	if	IN
en-wikipedia-org-3337	58	8	the	the	DT
en-wikipedia-org-3337	58	9	set	set	NN
en-wikipedia-org-3337	58	10	of	of	IN
en-wikipedia-org-3337	58	11	choices	choice	NNS
en-wikipedia-org-3337	58	12	is	be	VBZ
en-wikipedia-org-3337	58	13	compact	compact	JJ
en-wikipedia-org-3337	58	14	with	with	IN
en-wikipedia-org-3337	58	15	each	each	DT
en-wikipedia-org-3337	58	16	player	player	NN
en-wikipedia-org-3337	58	17	's	's	POS
en-wikipedia-org-3337	58	18	payoff	payoff	NN
en-wikipedia-org-3337	58	19	continuous	continuous	JJ
en-wikipedia-org-3337	58	20	in	in	IN
en-wikipedia-org-3337	58	21	the	the	DT
en-wikipedia-org-3337	58	22	strategies	strategy	NNS
en-wikipedia-org-3337	58	23	of	of	IN
en-wikipedia-org-3337	58	24	all	all	PDT
en-wikipedia-org-3337	58	25	the	the	DT
en-wikipedia-org-3337	58	26	players	player	NNS
en-wikipedia-org-3337	58	27	.	.	.
en-wikipedia-org-3337	59	1	[	[	-LRB-
en-wikipedia-org-3337	59	2	16	16	CD
en-wikipedia-org-3337	59	3	]	]	-RRB-
en-wikipedia-org-3337	59	4	Examples[edit	examples[edit	LS
en-wikipedia-org-3337	59	5	]	]	-RRB-
en-wikipedia-org-3337	59	6	Coordination	coordination	NN
en-wikipedia-org-3337	59	7	game[edit	game[edit	NFP
en-wikipedia-org-3337	59	8	]	]	-RRB-
en-wikipedia-org-3337	59	9	Main	main	JJ
en-wikipedia-org-3337	59	10	article	article	NN
en-wikipedia-org-3337	59	11	:	:	:
en-wikipedia-org-3337	59	12	Coordination	coordination	NN
en-wikipedia-org-3337	59	13	game	game	NN
en-wikipedia-org-3337	59	14	A	a	DT
en-wikipedia-org-3337	59	15	sample	sample	NN
en-wikipedia-org-3337	59	16	coordination	coordination	NN
en-wikipedia-org-3337	59	17	game	game	NN
en-wikipedia-org-3337	59	18	showing	show	VBG
en-wikipedia-org-3337	59	19	relative	relative	JJ
en-wikipedia-org-3337	59	20	payoff	payoff	NN
en-wikipedia-org-3337	59	21	for	for	IN
en-wikipedia-org-3337	59	22	player	player	NN
en-wikipedia-org-3337	59	23	1	1	CD
en-wikipedia-org-3337	59	24	(	(	-LRB-
en-wikipedia-org-3337	59	25	row	row	NN
en-wikipedia-org-3337	59	26	)	)	-RRB-
en-wikipedia-org-3337	59	27	/	/	SYM
en-wikipedia-org-3337	59	28	player	player	NN
en-wikipedia-org-3337	59	29	2	2	CD
en-wikipedia-org-3337	59	30	(	(	-LRB-
en-wikipedia-org-3337	59	31	column	column	NN
en-wikipedia-org-3337	59	32	)	)	-RRB-
en-wikipedia-org-3337	59	33	with	with	IN
en-wikipedia-org-3337	59	34	each	each	DT
en-wikipedia-org-3337	59	35	combination	combination	NN
en-wikipedia-org-3337	59	36	Player	Player	NNP
en-wikipedia-org-3337	59	37	2	2	CD
en-wikipedia-org-3337	59	38	Player	Player	NNP
en-wikipedia-org-3337	59	39	1	1	CD
en-wikipedia-org-3337	59	40	Player	Player	NNP
en-wikipedia-org-3337	59	41	2	2	CD
en-wikipedia-org-3337	59	42	adopts	adopt	VBZ
en-wikipedia-org-3337	59	43	strategy	strategy	NN
en-wikipedia-org-3337	59	44	A	a	DT
en-wikipedia-org-3337	59	45	Player	Player	NNP
en-wikipedia-org-3337	59	46	2	2	CD
en-wikipedia-org-3337	59	47	adopts	adopt	VBZ
en-wikipedia-org-3337	59	48	strategy	strategy	NN
en-wikipedia-org-3337	59	49	B	B	NNP
en-wikipedia-org-3337	59	50	Player	Player	NNP
en-wikipedia-org-3337	59	51	1	1	CD
en-wikipedia-org-3337	59	52	adopts	adopt	VBZ
en-wikipedia-org-3337	59	53	strategy	strategy	NN
en-wikipedia-org-3337	59	54	A	a	DT
en-wikipedia-org-3337	59	55	4	4	CD
en-wikipedia-org-3337	59	56	4	4	CD
en-wikipedia-org-3337	59	57	3	3	CD
en-wikipedia-org-3337	59	58	1	1	CD
en-wikipedia-org-3337	59	59	Player	Player	NNP
en-wikipedia-org-3337	59	60	1	1	CD
en-wikipedia-org-3337	59	61	adopts	adopt	VBZ
en-wikipedia-org-3337	59	62	strategy	strategy	NN
en-wikipedia-org-3337	59	63	B	b	NN
en-wikipedia-org-3337	59	64	1	1	CD
en-wikipedia-org-3337	59	65	3	3	CD
en-wikipedia-org-3337	59	66	2	2	CD
en-wikipedia-org-3337	59	67	2	2	CD
en-wikipedia-org-3337	59	68	The	the	DT
en-wikipedia-org-3337	59	69	coordination	coordination	NN
en-wikipedia-org-3337	59	70	game	game	NN
en-wikipedia-org-3337	59	71	is	be	VBZ
en-wikipedia-org-3337	59	72	a	a	DT
en-wikipedia-org-3337	59	73	classic	classic	JJ
en-wikipedia-org-3337	59	74	(	(	-LRB-
en-wikipedia-org-3337	59	75	symmetric	symmetric	JJ
en-wikipedia-org-3337	59	76	)	)	-RRB-
en-wikipedia-org-3337	59	77	two	two	CD
en-wikipedia-org-3337	59	78	player	player	NN
en-wikipedia-org-3337	59	79	,	,	,
en-wikipedia-org-3337	59	80	two	two	CD
en-wikipedia-org-3337	59	81	strategy	strategy	NN
en-wikipedia-org-3337	59	82	game	game	NN
en-wikipedia-org-3337	59	83	,	,	,
en-wikipedia-org-3337	59	84	with	with	IN
en-wikipedia-org-3337	59	85	an	an	DT
en-wikipedia-org-3337	59	86	example	example	NN
en-wikipedia-org-3337	59	87	payoff	payoff	NN
en-wikipedia-org-3337	59	88	matrix	matrix	NN
en-wikipedia-org-3337	59	89	shown	show	VBN
en-wikipedia-org-3337	59	90	to	to	IN
en-wikipedia-org-3337	59	91	the	the	DT
en-wikipedia-org-3337	59	92	right	right	NN
en-wikipedia-org-3337	59	93	.	.	.
en-wikipedia-org-3337	60	1	The	the	DT
en-wikipedia-org-3337	60	2	players	player	NNS
en-wikipedia-org-3337	60	3	should	should	MD
en-wikipedia-org-3337	60	4	thus	thus	RB
en-wikipedia-org-3337	60	5	coordinate	coordinate	VB
en-wikipedia-org-3337	60	6	,	,	,
en-wikipedia-org-3337	60	7	both	both	DT
en-wikipedia-org-3337	60	8	adopting	adopt	VBG
en-wikipedia-org-3337	60	9	strategy	strategy	NN
en-wikipedia-org-3337	60	10	A	a	DT
en-wikipedia-org-3337	60	11	,	,	,
en-wikipedia-org-3337	60	12	to	to	TO
en-wikipedia-org-3337	60	13	receive	receive	VB
en-wikipedia-org-3337	60	14	the	the	DT
en-wikipedia-org-3337	60	15	highest	high	JJS
en-wikipedia-org-3337	60	16	payoff	payoff	NN
en-wikipedia-org-3337	60	17	;	;	,
en-wikipedia-org-3337	60	18	i.e.	i.e.	FW
en-wikipedia-org-3337	60	19	,	,	,
en-wikipedia-org-3337	60	20	4	4	CD
en-wikipedia-org-3337	60	21	.	.	.
en-wikipedia-org-3337	61	1	If	if	IN
en-wikipedia-org-3337	61	2	both	both	DT
en-wikipedia-org-3337	61	3	players	player	NNS
en-wikipedia-org-3337	61	4	chose	choose	VBD
en-wikipedia-org-3337	61	5	strategy	strategy	NN
en-wikipedia-org-3337	61	6	B	b	NN
en-wikipedia-org-3337	61	7	though	though	RB
en-wikipedia-org-3337	61	8	,	,	,
en-wikipedia-org-3337	61	9	there	there	EX
en-wikipedia-org-3337	61	10	is	be	VBZ
en-wikipedia-org-3337	61	11	still	still	RB
en-wikipedia-org-3337	61	12	a	a	DT
en-wikipedia-org-3337	61	13	Nash	Nash	NNP
en-wikipedia-org-3337	61	14	equilibrium	equilibrium	NN
en-wikipedia-org-3337	61	15	.	.	.
en-wikipedia-org-3337	62	1	Although	although	IN
en-wikipedia-org-3337	62	2	each	each	DT
en-wikipedia-org-3337	62	3	player	player	NN
en-wikipedia-org-3337	62	4	is	be	VBZ
en-wikipedia-org-3337	62	5	awarded	award	VBN
en-wikipedia-org-3337	62	6	less	less	JJR
en-wikipedia-org-3337	62	7	than	than	IN
en-wikipedia-org-3337	62	8	optimal	optimal	JJ
en-wikipedia-org-3337	62	9	payoff	payoff	NN
en-wikipedia-org-3337	62	10	,	,	,
en-wikipedia-org-3337	62	11	neither	neither	CC
en-wikipedia-org-3337	62	12	player	player	NN
en-wikipedia-org-3337	62	13	has	have	VBZ
en-wikipedia-org-3337	62	14	incentive	incentive	NN
en-wikipedia-org-3337	62	15	to	to	TO
en-wikipedia-org-3337	62	16	change	change	VB
en-wikipedia-org-3337	62	17	strategy	strategy	NN
en-wikipedia-org-3337	62	18	due	due	JJ
en-wikipedia-org-3337	62	19	to	to	IN
en-wikipedia-org-3337	62	20	a	a	DT
en-wikipedia-org-3337	62	21	reduction	reduction	NN
en-wikipedia-org-3337	62	22	in	in	IN
en-wikipedia-org-3337	62	23	the	the	DT
en-wikipedia-org-3337	62	24	immediate	immediate	JJ
en-wikipedia-org-3337	62	25	payoff	payoff	NN
en-wikipedia-org-3337	62	26	(	(	-LRB-
en-wikipedia-org-3337	62	27	from	from	IN
en-wikipedia-org-3337	62	28	2	2	CD
en-wikipedia-org-3337	62	29	to	to	IN
en-wikipedia-org-3337	62	30	1	1	CD
en-wikipedia-org-3337	62	31	)	)	-RRB-
en-wikipedia-org-3337	62	32	.	.	.
en-wikipedia-org-3337	63	1	A	a	DT
en-wikipedia-org-3337	63	2	famous	famous	JJ
en-wikipedia-org-3337	63	3	example	example	NN
en-wikipedia-org-3337	63	4	of	of	IN
en-wikipedia-org-3337	63	5	this	this	DT
en-wikipedia-org-3337	63	6	type	type	NN
en-wikipedia-org-3337	63	7	of	of	IN
en-wikipedia-org-3337	63	8	game	game	NN
en-wikipedia-org-3337	63	9	was	be	VBD
en-wikipedia-org-3337	63	10	called	call	VBN
en-wikipedia-org-3337	63	11	the	the	DT
en-wikipedia-org-3337	63	12	stag	stag	JJ
en-wikipedia-org-3337	63	13	hunt	hunt	NN
en-wikipedia-org-3337	63	14	;	;	:
en-wikipedia-org-3337	63	15	in	in	IN
en-wikipedia-org-3337	63	16	the	the	DT
en-wikipedia-org-3337	63	17	game	game	NN
en-wikipedia-org-3337	63	18	two	two	CD
en-wikipedia-org-3337	63	19	players	player	NNS
en-wikipedia-org-3337	63	20	may	may	MD
en-wikipedia-org-3337	63	21	choose	choose	VB
en-wikipedia-org-3337	63	22	to	to	TO
en-wikipedia-org-3337	63	23	hunt	hunt	VB
en-wikipedia-org-3337	63	24	a	a	DT
en-wikipedia-org-3337	63	25	stag	stag	NN
en-wikipedia-org-3337	63	26	or	or	CC
en-wikipedia-org-3337	63	27	a	a	DT
en-wikipedia-org-3337	63	28	rabbit	rabbit	NN
en-wikipedia-org-3337	63	29	,	,	,
en-wikipedia-org-3337	63	30	the	the	DT
en-wikipedia-org-3337	63	31	former	former	JJ
en-wikipedia-org-3337	63	32	providing	provide	VBG
en-wikipedia-org-3337	63	33	more	more	JJR
en-wikipedia-org-3337	63	34	meat	meat	NN
en-wikipedia-org-3337	63	35	(	(	-LRB-
en-wikipedia-org-3337	63	36	4	4	CD
en-wikipedia-org-3337	63	37	utility	utility	NN
en-wikipedia-org-3337	63	38	units	unit	NNS
en-wikipedia-org-3337	63	39	)	)	-RRB-
en-wikipedia-org-3337	63	40	than	than	IN
en-wikipedia-org-3337	63	41	the	the	DT
en-wikipedia-org-3337	63	42	latter	latter	JJ
en-wikipedia-org-3337	63	43	(	(	-LRB-
en-wikipedia-org-3337	63	44	1	1	CD
en-wikipedia-org-3337	63	45	utility	utility	NN
en-wikipedia-org-3337	63	46	unit	unit	NN
en-wikipedia-org-3337	63	47	)	)	-RRB-
en-wikipedia-org-3337	63	48	.	.	.
en-wikipedia-org-3337	64	1	The	the	DT
en-wikipedia-org-3337	64	2	caveat	caveat	NN
en-wikipedia-org-3337	64	3	is	be	VBZ
en-wikipedia-org-3337	64	4	that	that	IN
en-wikipedia-org-3337	64	5	the	the	DT
en-wikipedia-org-3337	64	6	stag	stag	NN
en-wikipedia-org-3337	64	7	must	must	MD
en-wikipedia-org-3337	64	8	be	be	VB
en-wikipedia-org-3337	64	9	cooperatively	cooperatively	RB
en-wikipedia-org-3337	64	10	hunted	hunt	VBN
en-wikipedia-org-3337	64	11	,	,	,
en-wikipedia-org-3337	64	12	so	so	CC
en-wikipedia-org-3337	64	13	if	if	IN
en-wikipedia-org-3337	64	14	one	one	CD
en-wikipedia-org-3337	64	15	player	player	NN
en-wikipedia-org-3337	64	16	attempts	attempt	VBZ
en-wikipedia-org-3337	64	17	to	to	TO
en-wikipedia-org-3337	64	18	hunt	hunt	VB
en-wikipedia-org-3337	64	19	the	the	DT
en-wikipedia-org-3337	64	20	stag	stag	NN
en-wikipedia-org-3337	64	21	,	,	,
en-wikipedia-org-3337	64	22	while	while	IN
en-wikipedia-org-3337	64	23	the	the	DT
en-wikipedia-org-3337	64	24	other	other	JJ
en-wikipedia-org-3337	64	25	hunts	hunt	NNS
en-wikipedia-org-3337	64	26	the	the	DT
en-wikipedia-org-3337	64	27	rabbit	rabbit	NN
en-wikipedia-org-3337	64	28	,	,	,
en-wikipedia-org-3337	64	29	she	-PRON-	PRP
en-wikipedia-org-3337	64	30	/	/	SYM
en-wikipedia-org-3337	64	31	he	-PRON-	PRP
en-wikipedia-org-3337	64	32	will	will	MD
en-wikipedia-org-3337	64	33	fail	fail	VB
en-wikipedia-org-3337	64	34	in	in	IN
en-wikipedia-org-3337	64	35	hunting	hunting	NN
en-wikipedia-org-3337	64	36	(	(	-LRB-
en-wikipedia-org-3337	64	37	0	0	CD
en-wikipedia-org-3337	64	38	utility	utility	NN
en-wikipedia-org-3337	64	39	units	unit	NNS
en-wikipedia-org-3337	64	40	)	)	-RRB-
en-wikipedia-org-3337	64	41	,	,	,
en-wikipedia-org-3337	64	42	whereas	whereas	IN
en-wikipedia-org-3337	64	43	if	if	IN
en-wikipedia-org-3337	64	44	they	-PRON-	PRP
en-wikipedia-org-3337	64	45	both	both	DT
en-wikipedia-org-3337	64	46	hunt	hunt	VBP
en-wikipedia-org-3337	64	47	it	-PRON-	PRP
en-wikipedia-org-3337	64	48	they	-PRON-	PRP
en-wikipedia-org-3337	64	49	will	will	MD
en-wikipedia-org-3337	64	50	split	split	VB
en-wikipedia-org-3337	64	51	the	the	DT
en-wikipedia-org-3337	64	52	payoff	payoff	NN
en-wikipedia-org-3337	64	53	(	(	-LRB-
en-wikipedia-org-3337	64	54	2	2	CD
en-wikipedia-org-3337	64	55	,	,	,
en-wikipedia-org-3337	64	56	2	2	CD
en-wikipedia-org-3337	64	57	)	)	-RRB-
en-wikipedia-org-3337	64	58	.	.	.
en-wikipedia-org-3337	65	1	The	the	DT
en-wikipedia-org-3337	65	2	game	game	NN
en-wikipedia-org-3337	65	3	hence	hence	RB
en-wikipedia-org-3337	65	4	exhibits	exhibit	VBZ
en-wikipedia-org-3337	65	5	two	two	CD
en-wikipedia-org-3337	65	6	equilibria	equilibrium	NNS
en-wikipedia-org-3337	65	7	at	at	IN
en-wikipedia-org-3337	65	8	(	(	-LRB-
en-wikipedia-org-3337	65	9	stag	stag	JJ
en-wikipedia-org-3337	65	10	,	,	,
en-wikipedia-org-3337	65	11	stag	stag	JJ
en-wikipedia-org-3337	65	12	)	)	-RRB-
en-wikipedia-org-3337	65	13	and	and	CC
en-wikipedia-org-3337	65	14	(	(	-LRB-
en-wikipedia-org-3337	65	15	rabbit	rabbit	NN
en-wikipedia-org-3337	65	16	,	,	,
en-wikipedia-org-3337	65	17	rabbit	rabbit	NN
en-wikipedia-org-3337	65	18	)	)	-RRB-
en-wikipedia-org-3337	65	19	and	and	CC
en-wikipedia-org-3337	65	20	hence	hence	RB
en-wikipedia-org-3337	65	21	the	the	DT
en-wikipedia-org-3337	65	22	players	player	NNS
en-wikipedia-org-3337	65	23	'	'	POS
en-wikipedia-org-3337	65	24	optimal	optimal	JJ
en-wikipedia-org-3337	65	25	strategy	strategy	NN
en-wikipedia-org-3337	65	26	depend	depend	VBP
en-wikipedia-org-3337	65	27	on	on	IN
en-wikipedia-org-3337	65	28	their	-PRON-	PRP$
en-wikipedia-org-3337	65	29	expectation	expectation	NN
en-wikipedia-org-3337	65	30	on	on	IN
en-wikipedia-org-3337	65	31	what	what	WP
en-wikipedia-org-3337	65	32	the	the	DT
en-wikipedia-org-3337	65	33	other	other	JJ
en-wikipedia-org-3337	65	34	player	player	NN
en-wikipedia-org-3337	65	35	may	may	MD
en-wikipedia-org-3337	65	36	do	do	VB
en-wikipedia-org-3337	65	37	.	.	.
en-wikipedia-org-3337	66	1	If	if	IN
en-wikipedia-org-3337	66	2	one	one	CD
en-wikipedia-org-3337	66	3	hunter	hunter	NN
en-wikipedia-org-3337	66	4	trusts	trust	VBZ
en-wikipedia-org-3337	66	5	that	that	IN
en-wikipedia-org-3337	66	6	the	the	DT
en-wikipedia-org-3337	66	7	other	other	JJ
en-wikipedia-org-3337	66	8	will	will	MD
en-wikipedia-org-3337	66	9	hunt	hunt	VB
en-wikipedia-org-3337	66	10	the	the	DT
en-wikipedia-org-3337	66	11	stag	stag	NN
en-wikipedia-org-3337	66	12	,	,	,
en-wikipedia-org-3337	66	13	they	-PRON-	PRP
en-wikipedia-org-3337	66	14	should	should	MD
en-wikipedia-org-3337	66	15	hunt	hunt	VB
en-wikipedia-org-3337	66	16	the	the	DT
en-wikipedia-org-3337	66	17	stag	stag	NN
en-wikipedia-org-3337	66	18	;	;	:
en-wikipedia-org-3337	66	19	however	however	RB
en-wikipedia-org-3337	66	20	if	if	IN
en-wikipedia-org-3337	66	21	they	-PRON-	PRP
en-wikipedia-org-3337	66	22	suspect	suspect	VBP
en-wikipedia-org-3337	66	23	that	that	IN
en-wikipedia-org-3337	66	24	the	the	DT
en-wikipedia-org-3337	66	25	other	other	JJ
en-wikipedia-org-3337	66	26	will	will	MD
en-wikipedia-org-3337	66	27	hunt	hunt	VB
en-wikipedia-org-3337	66	28	the	the	DT
en-wikipedia-org-3337	66	29	rabbit	rabbit	NN
en-wikipedia-org-3337	66	30	,	,	,
en-wikipedia-org-3337	66	31	they	-PRON-	PRP
en-wikipedia-org-3337	66	32	should	should	MD
en-wikipedia-org-3337	66	33	hunt	hunt	VB
en-wikipedia-org-3337	66	34	the	the	DT
en-wikipedia-org-3337	66	35	rabbit	rabbit	NN
en-wikipedia-org-3337	66	36	.	.	.
en-wikipedia-org-3337	67	1	This	this	DT
en-wikipedia-org-3337	67	2	game	game	NN
en-wikipedia-org-3337	67	3	was	be	VBD
en-wikipedia-org-3337	67	4	used	use	VBN
en-wikipedia-org-3337	67	5	as	as	IN
en-wikipedia-org-3337	67	6	an	an	DT
en-wikipedia-org-3337	67	7	analogy	analogy	NN
en-wikipedia-org-3337	67	8	for	for	IN
en-wikipedia-org-3337	67	9	social	social	JJ
en-wikipedia-org-3337	67	10	cooperation	cooperation	NN
en-wikipedia-org-3337	67	11	,	,	,
en-wikipedia-org-3337	67	12	since	since	IN
en-wikipedia-org-3337	67	13	much	much	JJ
en-wikipedia-org-3337	67	14	of	of	IN
en-wikipedia-org-3337	67	15	the	the	DT
en-wikipedia-org-3337	67	16	benefit	benefit	NN
en-wikipedia-org-3337	67	17	that	that	WDT
en-wikipedia-org-3337	67	18	people	people	NNS
en-wikipedia-org-3337	67	19	gain	gain	VBP
en-wikipedia-org-3337	67	20	in	in	IN
en-wikipedia-org-3337	67	21	society	society	NN
en-wikipedia-org-3337	67	22	depends	depend	VBZ
en-wikipedia-org-3337	67	23	upon	upon	IN
en-wikipedia-org-3337	67	24	people	people	NNS
en-wikipedia-org-3337	67	25	cooperating	cooperate	VBG
en-wikipedia-org-3337	67	26	and	and	CC
en-wikipedia-org-3337	67	27	implicitly	implicitly	RB
en-wikipedia-org-3337	67	28	trusting	trust	VBG
en-wikipedia-org-3337	67	29	one	one	NN
en-wikipedia-org-3337	67	30	another	another	DT
en-wikipedia-org-3337	67	31	to	to	TO
en-wikipedia-org-3337	67	32	act	act	VB
en-wikipedia-org-3337	67	33	in	in	IN
en-wikipedia-org-3337	67	34	a	a	DT
en-wikipedia-org-3337	67	35	manner	manner	NN
en-wikipedia-org-3337	67	36	corresponding	correspond	VBG
en-wikipedia-org-3337	67	37	with	with	IN
en-wikipedia-org-3337	67	38	cooperation	cooperation	NN
en-wikipedia-org-3337	67	39	.	.	.
en-wikipedia-org-3337	68	1	Another	another	DT
en-wikipedia-org-3337	68	2	example	example	NN
en-wikipedia-org-3337	68	3	of	of	IN
en-wikipedia-org-3337	68	4	a	a	DT
en-wikipedia-org-3337	68	5	coordination	coordination	NN
en-wikipedia-org-3337	68	6	game	game	NN
en-wikipedia-org-3337	68	7	is	be	VBZ
en-wikipedia-org-3337	68	8	the	the	DT
en-wikipedia-org-3337	68	9	setting	setting	NN
en-wikipedia-org-3337	68	10	where	where	WRB
en-wikipedia-org-3337	68	11	two	two	CD
en-wikipedia-org-3337	68	12	technologies	technology	NNS
en-wikipedia-org-3337	68	13	are	be	VBP
en-wikipedia-org-3337	68	14	available	available	JJ
en-wikipedia-org-3337	68	15	to	to	IN
en-wikipedia-org-3337	68	16	two	two	CD
en-wikipedia-org-3337	68	17	firms	firm	NNS
en-wikipedia-org-3337	68	18	with	with	IN
en-wikipedia-org-3337	68	19	comparable	comparable	JJ
en-wikipedia-org-3337	68	20	products	product	NNS
en-wikipedia-org-3337	68	21	,	,	,
en-wikipedia-org-3337	68	22	and	and	CC
en-wikipedia-org-3337	68	23	they	-PRON-	PRP
en-wikipedia-org-3337	68	24	have	have	VBP
en-wikipedia-org-3337	68	25	to	to	TO
en-wikipedia-org-3337	68	26	elect	elect	VB
en-wikipedia-org-3337	68	27	a	a	DT
en-wikipedia-org-3337	68	28	strategy	strategy	NN
en-wikipedia-org-3337	68	29	to	to	TO
en-wikipedia-org-3337	68	30	become	become	VB
en-wikipedia-org-3337	68	31	the	the	DT
en-wikipedia-org-3337	68	32	market	market	NN
en-wikipedia-org-3337	68	33	standard	standard	NN
en-wikipedia-org-3337	68	34	.	.	.
en-wikipedia-org-3337	69	1	If	if	IN
en-wikipedia-org-3337	69	2	both	both	DT
en-wikipedia-org-3337	69	3	firms	firm	NNS
en-wikipedia-org-3337	69	4	agree	agree	VBP
en-wikipedia-org-3337	69	5	on	on	IN
en-wikipedia-org-3337	69	6	the	the	DT
en-wikipedia-org-3337	69	7	chosen	choose	VBN
en-wikipedia-org-3337	69	8	technology	technology	NN
en-wikipedia-org-3337	69	9	,	,	,
en-wikipedia-org-3337	69	10	high	high	JJ
en-wikipedia-org-3337	69	11	sales	sale	NNS
en-wikipedia-org-3337	69	12	are	be	VBP
en-wikipedia-org-3337	69	13	expected	expect	VBN
en-wikipedia-org-3337	69	14	for	for	IN
en-wikipedia-org-3337	69	15	both	both	DT
en-wikipedia-org-3337	69	16	firms	firm	NNS
en-wikipedia-org-3337	69	17	.	.	.
en-wikipedia-org-3337	70	1	If	if	IN
en-wikipedia-org-3337	70	2	the	the	DT
en-wikipedia-org-3337	70	3	firms	firm	NNS
en-wikipedia-org-3337	70	4	do	do	VBP
en-wikipedia-org-3337	70	5	not	not	RB
en-wikipedia-org-3337	70	6	agree	agree	VB
en-wikipedia-org-3337	70	7	on	on	IN
en-wikipedia-org-3337	70	8	the	the	DT
en-wikipedia-org-3337	70	9	standard	standard	JJ
en-wikipedia-org-3337	70	10	technology	technology	NN
en-wikipedia-org-3337	70	11	,	,	,
en-wikipedia-org-3337	70	12	few	few	JJ
en-wikipedia-org-3337	70	13	sales	sale	NNS
en-wikipedia-org-3337	70	14	result	result	VBP
en-wikipedia-org-3337	70	15	.	.	.
en-wikipedia-org-3337	71	1	Both	both	DT
en-wikipedia-org-3337	71	2	strategies	strategy	NNS
en-wikipedia-org-3337	71	3	are	be	VBP
en-wikipedia-org-3337	71	4	Nash	Nash	NNP
en-wikipedia-org-3337	71	5	equilibria	equilibria	NN
en-wikipedia-org-3337	71	6	of	of	IN
en-wikipedia-org-3337	71	7	the	the	DT
en-wikipedia-org-3337	71	8	game	game	NN
en-wikipedia-org-3337	71	9	.	.	.
en-wikipedia-org-3337	72	1	Driving	drive	VBG
en-wikipedia-org-3337	72	2	on	on	IN
en-wikipedia-org-3337	72	3	a	a	DT
en-wikipedia-org-3337	72	4	road	road	NN
en-wikipedia-org-3337	72	5	against	against	IN
en-wikipedia-org-3337	72	6	an	an	DT
en-wikipedia-org-3337	72	7	oncoming	oncoming	JJ
en-wikipedia-org-3337	72	8	car	car	NN
en-wikipedia-org-3337	72	9	,	,	,
en-wikipedia-org-3337	72	10	and	and	CC
en-wikipedia-org-3337	72	11	having	have	VBG
en-wikipedia-org-3337	72	12	to	to	TO
en-wikipedia-org-3337	72	13	choose	choose	VB
en-wikipedia-org-3337	72	14	either	either	CC
en-wikipedia-org-3337	72	15	to	to	TO
en-wikipedia-org-3337	72	16	swerve	swerve	VB
en-wikipedia-org-3337	72	17	on	on	IN
en-wikipedia-org-3337	72	18	the	the	DT
en-wikipedia-org-3337	72	19	left	left	NN
en-wikipedia-org-3337	72	20	or	or	CC
en-wikipedia-org-3337	72	21	to	to	TO
en-wikipedia-org-3337	72	22	swerve	swerve	VB
en-wikipedia-org-3337	72	23	on	on	IN
en-wikipedia-org-3337	72	24	the	the	DT
en-wikipedia-org-3337	72	25	right	right	NN
en-wikipedia-org-3337	72	26	of	of	IN
en-wikipedia-org-3337	72	27	the	the	DT
en-wikipedia-org-3337	72	28	road	road	NN
en-wikipedia-org-3337	72	29	,	,	,
en-wikipedia-org-3337	72	30	is	be	VBZ
en-wikipedia-org-3337	72	31	also	also	RB
en-wikipedia-org-3337	72	32	a	a	DT
en-wikipedia-org-3337	72	33	coordination	coordination	NN
en-wikipedia-org-3337	72	34	game	game	NN
en-wikipedia-org-3337	72	35	.	.	.
en-wikipedia-org-3337	73	1	For	for	IN
en-wikipedia-org-3337	73	2	example	example	NN
en-wikipedia-org-3337	73	3	,	,	,
en-wikipedia-org-3337	73	4	with	with	IN
en-wikipedia-org-3337	73	5	payoffs	payoff	NNS
en-wikipedia-org-3337	73	6	10	10	CD
en-wikipedia-org-3337	73	7	meaning	mean	VBG
en-wikipedia-org-3337	73	8	no	no	DT
en-wikipedia-org-3337	73	9	crash	crash	NN
en-wikipedia-org-3337	73	10	and	and	CC
en-wikipedia-org-3337	73	11	0	0	NFP
en-wikipedia-org-3337	73	12	meaning	mean	VBG
en-wikipedia-org-3337	73	13	a	a	DT
en-wikipedia-org-3337	73	14	crash	crash	NN
en-wikipedia-org-3337	73	15	,	,	,
en-wikipedia-org-3337	73	16	the	the	DT
en-wikipedia-org-3337	73	17	coordination	coordination	NN
en-wikipedia-org-3337	73	18	game	game	NN
en-wikipedia-org-3337	73	19	can	can	MD
en-wikipedia-org-3337	73	20	be	be	VB
en-wikipedia-org-3337	73	21	defined	define	VBN
en-wikipedia-org-3337	73	22	with	with	IN
en-wikipedia-org-3337	73	23	the	the	DT
en-wikipedia-org-3337	73	24	following	follow	VBG
en-wikipedia-org-3337	73	25	payoff	payoff	NN
en-wikipedia-org-3337	73	26	matrix	matrix	NN
en-wikipedia-org-3337	73	27	:	:	:
en-wikipedia-org-3337	73	28	The	the	DT
en-wikipedia-org-3337	73	29	driving	drive	VBG
en-wikipedia-org-3337	73	30	game	game	NN
en-wikipedia-org-3337	73	31	Driver	driver	NN
en-wikipedia-org-3337	73	32	2	2	CD
en-wikipedia-org-3337	73	33	Driver	driver	NN
en-wikipedia-org-3337	73	34	1	1	CD
en-wikipedia-org-3337	73	35	Drive	drive	NN
en-wikipedia-org-3337	73	36	on	on	IN
en-wikipedia-org-3337	73	37	the	the	DT
en-wikipedia-org-3337	73	38	Left	left	JJ
en-wikipedia-org-3337	73	39	Drive	Drive	NNP
en-wikipedia-org-3337	73	40	on	on	IN
en-wikipedia-org-3337	73	41	the	the	DT
en-wikipedia-org-3337	73	42	Right	Right	NNP
en-wikipedia-org-3337	73	43	Drive	Drive	NNP
en-wikipedia-org-3337	73	44	on	on	IN
en-wikipedia-org-3337	73	45	the	the	DT
en-wikipedia-org-3337	73	46	Left	leave	VBN
en-wikipedia-org-3337	73	47	10	10	CD
en-wikipedia-org-3337	73	48	10	10	CD
en-wikipedia-org-3337	73	49	0	0	CD
en-wikipedia-org-3337	73	50	0	0	CD
en-wikipedia-org-3337	73	51	Drive	drive	NN
en-wikipedia-org-3337	73	52	on	on	IN
en-wikipedia-org-3337	73	53	the	the	DT
en-wikipedia-org-3337	73	54	Right	right	JJ
en-wikipedia-org-3337	73	55	0	0	CD
en-wikipedia-org-3337	73	56	0	0	CD
en-wikipedia-org-3337	73	57	10	10	CD
en-wikipedia-org-3337	73	58	10	10	CD
en-wikipedia-org-3337	73	59	In	in	IN
en-wikipedia-org-3337	73	60	this	this	DT
en-wikipedia-org-3337	73	61	case	case	NN
en-wikipedia-org-3337	73	62	there	there	EX
en-wikipedia-org-3337	73	63	are	be	VBP
en-wikipedia-org-3337	73	64	two	two	CD
en-wikipedia-org-3337	73	65	pure	pure	JJ
en-wikipedia-org-3337	73	66	-	-	HYPH
en-wikipedia-org-3337	73	67	strategy	strategy	NN
en-wikipedia-org-3337	73	68	Nash	Nash	NNP
en-wikipedia-org-3337	73	69	equilibria	equilibria	NN
en-wikipedia-org-3337	73	70	,	,	,
en-wikipedia-org-3337	73	71	when	when	WRB
en-wikipedia-org-3337	73	72	both	both	DT
en-wikipedia-org-3337	73	73	choose	choose	VBP
en-wikipedia-org-3337	73	74	to	to	IN
en-wikipedia-org-3337	73	75	either	either	DT
en-wikipedia-org-3337	73	76	drive	drive	VB
en-wikipedia-org-3337	73	77	on	on	IN
en-wikipedia-org-3337	73	78	the	the	DT
en-wikipedia-org-3337	73	79	left	left	NN
en-wikipedia-org-3337	73	80	or	or	CC
en-wikipedia-org-3337	73	81	on	on	IN
en-wikipedia-org-3337	73	82	the	the	DT
en-wikipedia-org-3337	73	83	right	right	NN
en-wikipedia-org-3337	73	84	.	.	.
en-wikipedia-org-3337	74	1	If	if	IN
en-wikipedia-org-3337	74	2	we	-PRON-	PRP
en-wikipedia-org-3337	74	3	admit	admit	VBP
en-wikipedia-org-3337	74	4	mixed	mixed	JJ
en-wikipedia-org-3337	74	5	strategies	strategy	NNS
en-wikipedia-org-3337	74	6	(	(	-LRB-
en-wikipedia-org-3337	74	7	where	where	WRB
en-wikipedia-org-3337	74	8	a	a	DT
en-wikipedia-org-3337	74	9	pure	pure	JJ
en-wikipedia-org-3337	74	10	strategy	strategy	NN
en-wikipedia-org-3337	74	11	is	be	VBZ
en-wikipedia-org-3337	74	12	chosen	choose	VBN
en-wikipedia-org-3337	74	13	at	at	IN
en-wikipedia-org-3337	74	14	random	random	JJ
en-wikipedia-org-3337	74	15	,	,	,
en-wikipedia-org-3337	74	16	subject	subject	JJ
en-wikipedia-org-3337	74	17	to	to	IN
en-wikipedia-org-3337	74	18	some	some	DT
en-wikipedia-org-3337	74	19	fixed	fix	VBN
en-wikipedia-org-3337	74	20	probability	probability	NN
en-wikipedia-org-3337	74	21	)	)	-RRB-
en-wikipedia-org-3337	74	22	,	,	,
en-wikipedia-org-3337	74	23	then	then	RB
en-wikipedia-org-3337	74	24	there	there	EX
en-wikipedia-org-3337	74	25	are	be	VBP
en-wikipedia-org-3337	74	26	three	three	CD
en-wikipedia-org-3337	74	27	Nash	Nash	NNP
en-wikipedia-org-3337	74	28	equilibria	equilibria	NN
en-wikipedia-org-3337	74	29	for	for	IN
en-wikipedia-org-3337	74	30	the	the	DT
en-wikipedia-org-3337	74	31	same	same	JJ
en-wikipedia-org-3337	74	32	case	case	NN
en-wikipedia-org-3337	74	33	:	:	:
en-wikipedia-org-3337	74	34	two	two	CD
en-wikipedia-org-3337	74	35	we	-PRON-	PRP
en-wikipedia-org-3337	74	36	have	have	VBP
en-wikipedia-org-3337	74	37	seen	see	VBN
en-wikipedia-org-3337	74	38	from	from	IN
en-wikipedia-org-3337	74	39	the	the	DT
en-wikipedia-org-3337	74	40	pure	pure	JJ
en-wikipedia-org-3337	74	41	-	-	HYPH
en-wikipedia-org-3337	74	42	strategy	strategy	NN
en-wikipedia-org-3337	74	43	form	form	NN
en-wikipedia-org-3337	74	44	,	,	,
en-wikipedia-org-3337	74	45	where	where	WRB
en-wikipedia-org-3337	74	46	the	the	DT
en-wikipedia-org-3337	74	47	probabilities	probability	NNS
en-wikipedia-org-3337	74	48	are	be	VBP
en-wikipedia-org-3337	74	49	(	(	-LRB-
en-wikipedia-org-3337	74	50	0	0	CD
en-wikipedia-org-3337	74	51	%	%	NN
en-wikipedia-org-3337	74	52	,	,	,
en-wikipedia-org-3337	74	53	100	100	CD
en-wikipedia-org-3337	74	54	%	%	NN
en-wikipedia-org-3337	74	55	)	)	-RRB-
en-wikipedia-org-3337	74	56	for	for	IN
en-wikipedia-org-3337	74	57	player	player	NN
en-wikipedia-org-3337	74	58	one	one	CD
en-wikipedia-org-3337	74	59	,	,	,
en-wikipedia-org-3337	74	60	(	(	-LRB-
en-wikipedia-org-3337	74	61	0	0	CD
en-wikipedia-org-3337	74	62	%	%	NN
en-wikipedia-org-3337	74	63	,	,	,
en-wikipedia-org-3337	74	64	100	100	CD
en-wikipedia-org-3337	74	65	%	%	NN
en-wikipedia-org-3337	74	66	)	)	-RRB-
en-wikipedia-org-3337	74	67	for	for	IN
en-wikipedia-org-3337	74	68	player	player	NN
en-wikipedia-org-3337	74	69	two	two	CD
en-wikipedia-org-3337	74	70	;	;	:
en-wikipedia-org-3337	74	71	and	and	CC
en-wikipedia-org-3337	74	72	(	(	-LRB-
en-wikipedia-org-3337	74	73	100	100	CD
en-wikipedia-org-3337	74	74	%	%	NN
en-wikipedia-org-3337	74	75	,	,	,
en-wikipedia-org-3337	74	76	0	0	CD
en-wikipedia-org-3337	74	77	%	%	NN
en-wikipedia-org-3337	74	78	)	)	-RRB-
en-wikipedia-org-3337	74	79	for	for	IN
en-wikipedia-org-3337	74	80	player	player	NN
en-wikipedia-org-3337	74	81	one	one	CD
en-wikipedia-org-3337	74	82	,	,	,
en-wikipedia-org-3337	74	83	(	(	-LRB-
en-wikipedia-org-3337	74	84	100	100	CD
en-wikipedia-org-3337	74	85	%	%	NN
en-wikipedia-org-3337	74	86	,	,	,
en-wikipedia-org-3337	74	87	0	0	CD
en-wikipedia-org-3337	74	88	%	%	NN
en-wikipedia-org-3337	74	89	)	)	-RRB-
en-wikipedia-org-3337	74	90	for	for	IN
en-wikipedia-org-3337	74	91	player	player	NN
en-wikipedia-org-3337	74	92	two	two	CD
en-wikipedia-org-3337	74	93	respectively	respectively	RB
en-wikipedia-org-3337	74	94	.	.	.
en-wikipedia-org-3337	75	1	We	-PRON-	PRP
en-wikipedia-org-3337	75	2	add	add	VBP
en-wikipedia-org-3337	75	3	another	another	DT
en-wikipedia-org-3337	75	4	where	where	WRB
en-wikipedia-org-3337	75	5	the	the	DT
en-wikipedia-org-3337	75	6	probabilities	probability	NNS
en-wikipedia-org-3337	75	7	for	for	IN
en-wikipedia-org-3337	75	8	each	each	DT
en-wikipedia-org-3337	75	9	player	player	NN
en-wikipedia-org-3337	75	10	are	be	VBP
en-wikipedia-org-3337	75	11	(	(	-LRB-
en-wikipedia-org-3337	75	12	50	50	CD
en-wikipedia-org-3337	75	13	%	%	NN
en-wikipedia-org-3337	75	14	,	,	,
en-wikipedia-org-3337	75	15	50	50	CD
en-wikipedia-org-3337	75	16	%	%	NN
en-wikipedia-org-3337	75	17	)	)	-RRB-
en-wikipedia-org-3337	75	18	.	.	.
en-wikipedia-org-3337	76	1	Prisoner	Prisoner	NNP
en-wikipedia-org-3337	76	2	's	's	POS
en-wikipedia-org-3337	76	3	dilemma[edit	dilemma[edit	NN
en-wikipedia-org-3337	76	4	]	]	-RRB-
en-wikipedia-org-3337	76	5	Main	main	JJ
en-wikipedia-org-3337	76	6	article	article	NN
en-wikipedia-org-3337	76	7	:	:	:
en-wikipedia-org-3337	76	8	Prisoner	Prisoner	NNP
en-wikipedia-org-3337	76	9	's	's	POS
en-wikipedia-org-3337	76	10	dilemma	dilemma	NN
en-wikipedia-org-3337	76	11	Example	Example	NNP
en-wikipedia-org-3337	76	12	PD	PD	NNP
en-wikipedia-org-3337	76	13	payoff	payoff	NN
en-wikipedia-org-3337	76	14	matrix	matrix	NN
en-wikipedia-org-3337	76	15	Prisoner	Prisoner	NNP
en-wikipedia-org-3337	76	16	2	2	CD
en-wikipedia-org-3337	76	17	Prisoner	prisoner	NN
en-wikipedia-org-3337	76	18	1	1	CD
en-wikipedia-org-3337	76	19	Cooperate	Cooperate	NNP
en-wikipedia-org-3337	76	20	(	(	-LRB-
en-wikipedia-org-3337	76	21	with	with	IN
en-wikipedia-org-3337	76	22	other	other	JJ
en-wikipedia-org-3337	76	23	)	)	-RRB-
en-wikipedia-org-3337	76	24	Defect	Defect	NNP
en-wikipedia-org-3337	76	25	(	(	-LRB-
en-wikipedia-org-3337	76	26	betray	betray	VB
en-wikipedia-org-3337	76	27	other	other	JJ
en-wikipedia-org-3337	76	28	)	)	-RRB-
en-wikipedia-org-3337	76	29	Cooperate	Cooperate	NNP
en-wikipedia-org-3337	76	30	(	(	-LRB-
en-wikipedia-org-3337	76	31	with	with	IN
en-wikipedia-org-3337	76	32	other	other	JJ
en-wikipedia-org-3337	76	33	)	)	-RRB-
en-wikipedia-org-3337	76	34	−1	−1	NNP
en-wikipedia-org-3337	76	35	,	,	,
en-wikipedia-org-3337	76	36	−1	−1	NNP
en-wikipedia-org-3337	76	37	−3	−3	NNP
en-wikipedia-org-3337	76	38	,	,	,
en-wikipedia-org-3337	76	39	0	0	NFP
en-wikipedia-org-3337	76	40	Defect	defect	JJ
en-wikipedia-org-3337	76	41	(	(	-LRB-
en-wikipedia-org-3337	76	42	betray	betray	VB
en-wikipedia-org-3337	76	43	other	other	JJ
en-wikipedia-org-3337	76	44	)	)	-RRB-
en-wikipedia-org-3337	76	45	0	0	NFP
en-wikipedia-org-3337	76	46	,	,	,
en-wikipedia-org-3337	76	47	−3	−3	NNP
en-wikipedia-org-3337	76	48	−2	−2	NNP
en-wikipedia-org-3337	76	49	,	,	,
en-wikipedia-org-3337	76	50	−2	−2	NNP
en-wikipedia-org-3337	76	51	Imagine	Imagine	NNP
en-wikipedia-org-3337	76	52	two	two	CD
en-wikipedia-org-3337	76	53	prisoners	prisoner	NNS
en-wikipedia-org-3337	76	54	held	hold	VBN
en-wikipedia-org-3337	76	55	in	in	IN
en-wikipedia-org-3337	76	56	separate	separate	JJ
en-wikipedia-org-3337	76	57	cells	cell	NNS
en-wikipedia-org-3337	76	58	,	,	,
en-wikipedia-org-3337	76	59	interrogated	interrogate	VBN
en-wikipedia-org-3337	76	60	simultaneously	simultaneously	RB
en-wikipedia-org-3337	76	61	,	,	,
en-wikipedia-org-3337	76	62	and	and	CC
en-wikipedia-org-3337	76	63	offered	offer	VBD
en-wikipedia-org-3337	76	64	deals	deal	NNS
en-wikipedia-org-3337	76	65	(	(	-LRB-
en-wikipedia-org-3337	76	66	lighter	light	JJR
en-wikipedia-org-3337	76	67	jail	jail	NN
en-wikipedia-org-3337	76	68	sentences	sentence	NNS
en-wikipedia-org-3337	76	69	)	)	-RRB-
en-wikipedia-org-3337	76	70	for	for	IN
en-wikipedia-org-3337	76	71	betraying	betray	VBG
en-wikipedia-org-3337	76	72	their	-PRON-	PRP$
en-wikipedia-org-3337	76	73	fellow	fellow	JJ
en-wikipedia-org-3337	76	74	criminal	criminal	NN
en-wikipedia-org-3337	76	75	.	.	.
en-wikipedia-org-3337	77	1	They	-PRON-	PRP
en-wikipedia-org-3337	77	2	can	can	MD
en-wikipedia-org-3337	77	3	"	"	``
en-wikipedia-org-3337	77	4	cooperate	cooperate	VB
en-wikipedia-org-3337	77	5	"	"	''
en-wikipedia-org-3337	77	6	(	(	-LRB-
en-wikipedia-org-3337	77	7	with	with	IN
en-wikipedia-org-3337	77	8	the	the	DT
en-wikipedia-org-3337	77	9	other	other	JJ
en-wikipedia-org-3337	77	10	prisoner	prisoner	NN
en-wikipedia-org-3337	77	11	)	)	-RRB-
en-wikipedia-org-3337	77	12	by	by	IN
en-wikipedia-org-3337	77	13	not	not	RB
en-wikipedia-org-3337	77	14	snitching	snitch	VBG
en-wikipedia-org-3337	77	15	,	,	,
en-wikipedia-org-3337	77	16	or	or	CC
en-wikipedia-org-3337	77	17	"	"	``
en-wikipedia-org-3337	77	18	defect	defect	VB
en-wikipedia-org-3337	77	19	"	"	''
en-wikipedia-org-3337	77	20	by	by	IN
en-wikipedia-org-3337	77	21	betraying	betray	VBG
en-wikipedia-org-3337	77	22	the	the	DT
en-wikipedia-org-3337	77	23	other	other	JJ
en-wikipedia-org-3337	77	24	.	.	.
en-wikipedia-org-3337	78	1	However	however	RB
en-wikipedia-org-3337	78	2	,	,	,
en-wikipedia-org-3337	78	3	there	there	EX
en-wikipedia-org-3337	78	4	is	be	VBZ
en-wikipedia-org-3337	78	5	a	a	DT
en-wikipedia-org-3337	78	6	catch	catch	NN
en-wikipedia-org-3337	78	7	;	;	:
en-wikipedia-org-3337	78	8	if	if	IN
en-wikipedia-org-3337	78	9	both	both	DT
en-wikipedia-org-3337	78	10	players	player	NNS
en-wikipedia-org-3337	78	11	defect	defect	VBP
en-wikipedia-org-3337	78	12	,	,	,
en-wikipedia-org-3337	78	13	then	then	RB
en-wikipedia-org-3337	78	14	they	-PRON-	PRP
en-wikipedia-org-3337	78	15	both	both	DT
en-wikipedia-org-3337	78	16	serve	serve	VBP
en-wikipedia-org-3337	78	17	a	a	DT
en-wikipedia-org-3337	78	18	longer	long	JJR
en-wikipedia-org-3337	78	19	sentence	sentence	NN
en-wikipedia-org-3337	78	20	than	than	IN
en-wikipedia-org-3337	78	21	if	if	IN
en-wikipedia-org-3337	78	22	neither	neither	DT
en-wikipedia-org-3337	78	23	said	say	VBD
en-wikipedia-org-3337	78	24	anything	anything	NN
en-wikipedia-org-3337	78	25	.	.	.
en-wikipedia-org-3337	79	1	Lower	low	JJR
en-wikipedia-org-3337	79	2	jail	jail	NN
en-wikipedia-org-3337	79	3	sentences	sentence	NNS
en-wikipedia-org-3337	79	4	are	be	VBP
en-wikipedia-org-3337	79	5	interpreted	interpret	VBN
en-wikipedia-org-3337	79	6	as	as	IN
en-wikipedia-org-3337	79	7	higher	high	JJR
en-wikipedia-org-3337	79	8	payoffs	payoff	NNS
en-wikipedia-org-3337	79	9	(	(	-LRB-
en-wikipedia-org-3337	79	10	shown	show	VBN
en-wikipedia-org-3337	79	11	in	in	IN
en-wikipedia-org-3337	79	12	the	the	DT
en-wikipedia-org-3337	79	13	table	table	NN
en-wikipedia-org-3337	79	14	)	)	-RRB-
en-wikipedia-org-3337	79	15	.	.	.
en-wikipedia-org-3337	80	1	The	the	DT
en-wikipedia-org-3337	80	2	prisoner	prisoner	NN
en-wikipedia-org-3337	80	3	's	's	POS
en-wikipedia-org-3337	80	4	dilemma	dilemma	NN
en-wikipedia-org-3337	80	5	has	have	VBZ
en-wikipedia-org-3337	80	6	a	a	DT
en-wikipedia-org-3337	80	7	similar	similar	JJ
en-wikipedia-org-3337	80	8	matrix	matrix	NN
en-wikipedia-org-3337	80	9	as	as	IN
en-wikipedia-org-3337	80	10	depicted	depict	VBN
en-wikipedia-org-3337	80	11	for	for	IN
en-wikipedia-org-3337	80	12	the	the	DT
en-wikipedia-org-3337	80	13	coordination	coordination	NN
en-wikipedia-org-3337	80	14	game	game	NN
en-wikipedia-org-3337	80	15	,	,	,
en-wikipedia-org-3337	80	16	but	but	CC
en-wikipedia-org-3337	80	17	the	the	DT
en-wikipedia-org-3337	80	18	maximum	maximum	JJ
en-wikipedia-org-3337	80	19	reward	reward	NN
en-wikipedia-org-3337	80	20	for	for	IN
en-wikipedia-org-3337	80	21	each	each	DT
en-wikipedia-org-3337	80	22	player	player	NN
en-wikipedia-org-3337	80	23	(	(	-LRB-
en-wikipedia-org-3337	80	24	in	in	IN
en-wikipedia-org-3337	80	25	this	this	DT
en-wikipedia-org-3337	80	26	case	case	NN
en-wikipedia-org-3337	80	27	,	,	,
en-wikipedia-org-3337	80	28	a	a	DT
en-wikipedia-org-3337	80	29	minimum	minimum	JJ
en-wikipedia-org-3337	80	30	loss	loss	NN
en-wikipedia-org-3337	80	31	of	of	IN
en-wikipedia-org-3337	80	32	0	0	CD
en-wikipedia-org-3337	80	33	)	)	-RRB-
en-wikipedia-org-3337	80	34	is	be	VBZ
en-wikipedia-org-3337	80	35	obtained	obtain	VBN
en-wikipedia-org-3337	80	36	only	only	RB
en-wikipedia-org-3337	80	37	when	when	WRB
en-wikipedia-org-3337	80	38	the	the	DT
en-wikipedia-org-3337	80	39	players	player	NNS
en-wikipedia-org-3337	80	40	'	'	POS
en-wikipedia-org-3337	80	41	decisions	decision	NNS
en-wikipedia-org-3337	80	42	are	be	VBP
en-wikipedia-org-3337	80	43	different	different	JJ
en-wikipedia-org-3337	80	44	.	.	.
en-wikipedia-org-3337	81	1	Each	each	DT
en-wikipedia-org-3337	81	2	player	player	NN
en-wikipedia-org-3337	81	3	improves	improve	VBZ
en-wikipedia-org-3337	81	4	their	-PRON-	PRP$
en-wikipedia-org-3337	81	5	own	own	JJ
en-wikipedia-org-3337	81	6	situation	situation	NN
en-wikipedia-org-3337	81	7	by	by	IN
en-wikipedia-org-3337	81	8	switching	switch	VBG
en-wikipedia-org-3337	81	9	from	from	IN
en-wikipedia-org-3337	81	10	"	"	``
en-wikipedia-org-3337	81	11	cooperating	cooperate	VBG
en-wikipedia-org-3337	81	12	"	"	''
en-wikipedia-org-3337	81	13	to	to	IN
en-wikipedia-org-3337	81	14	"	"	``
en-wikipedia-org-3337	81	15	defecting	defect	VBG
en-wikipedia-org-3337	81	16	"	"	''
en-wikipedia-org-3337	81	17	,	,	,
en-wikipedia-org-3337	81	18	given	give	VBN
en-wikipedia-org-3337	81	19	knowledge	knowledge	NN
en-wikipedia-org-3337	81	20	that	that	IN
en-wikipedia-org-3337	81	21	the	the	DT
en-wikipedia-org-3337	81	22	other	other	JJ
en-wikipedia-org-3337	81	23	player	player	NN
en-wikipedia-org-3337	81	24	's	's	POS
en-wikipedia-org-3337	81	25	best	good	JJS
en-wikipedia-org-3337	81	26	decision	decision	NN
en-wikipedia-org-3337	81	27	is	be	VBZ
en-wikipedia-org-3337	81	28	to	to	TO
en-wikipedia-org-3337	81	29	"	"	``
en-wikipedia-org-3337	81	30	defect	defect	VB
en-wikipedia-org-3337	81	31	"	"	''
en-wikipedia-org-3337	81	32	.	.	.
en-wikipedia-org-3337	82	1	The	the	DT
en-wikipedia-org-3337	82	2	prisoner	prisoner	NN
en-wikipedia-org-3337	82	3	's	's	POS
en-wikipedia-org-3337	82	4	dilemma	dilemma	NN
en-wikipedia-org-3337	82	5	thus	thus	RB
en-wikipedia-org-3337	82	6	has	have	VBZ
en-wikipedia-org-3337	82	7	a	a	DT
en-wikipedia-org-3337	82	8	single	single	JJ
en-wikipedia-org-3337	82	9	Nash	Nash	NNP
en-wikipedia-org-3337	82	10	equilibrium	equilibrium	NN
en-wikipedia-org-3337	82	11	:	:	:
en-wikipedia-org-3337	82	12	both	both	DT
en-wikipedia-org-3337	82	13	players	player	NNS
en-wikipedia-org-3337	82	14	choosing	choose	VBG
en-wikipedia-org-3337	82	15	to	to	TO
en-wikipedia-org-3337	82	16	defect	defect	VB
en-wikipedia-org-3337	82	17	.	.	.
en-wikipedia-org-3337	83	1	What	what	WP
en-wikipedia-org-3337	83	2	has	have	VBZ
en-wikipedia-org-3337	83	3	long	long	RB
en-wikipedia-org-3337	83	4	made	make	VBN
en-wikipedia-org-3337	83	5	this	this	DT
en-wikipedia-org-3337	83	6	an	an	DT
en-wikipedia-org-3337	83	7	interesting	interesting	JJ
en-wikipedia-org-3337	83	8	case	case	NN
en-wikipedia-org-3337	83	9	to	to	TO
en-wikipedia-org-3337	83	10	study	study	VB
en-wikipedia-org-3337	83	11	is	be	VBZ
en-wikipedia-org-3337	83	12	the	the	DT
en-wikipedia-org-3337	83	13	fact	fact	NN
en-wikipedia-org-3337	83	14	that	that	IN
en-wikipedia-org-3337	83	15	this	this	DT
en-wikipedia-org-3337	83	16	scenario	scenario	NN
en-wikipedia-org-3337	83	17	is	be	VBZ
en-wikipedia-org-3337	83	18	globally	globally	RB
en-wikipedia-org-3337	83	19	inferior	inferior	JJ
en-wikipedia-org-3337	83	20	to	to	TO
en-wikipedia-org-3337	83	21	"	"	``
en-wikipedia-org-3337	83	22	both	both	DT
en-wikipedia-org-3337	83	23	cooperating	cooperate	VBG
en-wikipedia-org-3337	83	24	"	"	''
en-wikipedia-org-3337	83	25	.	.	.
en-wikipedia-org-3337	84	1	That	that	RB
en-wikipedia-org-3337	84	2	is	is	RB
en-wikipedia-org-3337	84	3	,	,	,
en-wikipedia-org-3337	84	4	both	both	DT
en-wikipedia-org-3337	84	5	players	player	NNS
en-wikipedia-org-3337	84	6	would	would	MD
en-wikipedia-org-3337	84	7	be	be	VB
en-wikipedia-org-3337	84	8	better	well	JJR
en-wikipedia-org-3337	84	9	off	off	RP
en-wikipedia-org-3337	84	10	if	if	IN
en-wikipedia-org-3337	84	11	they	-PRON-	PRP
en-wikipedia-org-3337	84	12	both	both	DT
en-wikipedia-org-3337	84	13	chose	choose	VBD
en-wikipedia-org-3337	84	14	to	to	TO
en-wikipedia-org-3337	84	15	"	"	``
en-wikipedia-org-3337	84	16	cooperate	cooperate	VB
en-wikipedia-org-3337	84	17	"	"	''
en-wikipedia-org-3337	84	18	instead	instead	RB
en-wikipedia-org-3337	84	19	of	of	IN
en-wikipedia-org-3337	84	20	both	both	CC
en-wikipedia-org-3337	84	21	choosing	choose	VBG
en-wikipedia-org-3337	84	22	to	to	TO
en-wikipedia-org-3337	84	23	defect	defect	VB
en-wikipedia-org-3337	84	24	.	.	.
en-wikipedia-org-3337	85	1	However	however	RB
en-wikipedia-org-3337	85	2	,	,	,
en-wikipedia-org-3337	85	3	each	each	DT
en-wikipedia-org-3337	85	4	player	player	NN
en-wikipedia-org-3337	85	5	could	could	MD
en-wikipedia-org-3337	85	6	improve	improve	VB
en-wikipedia-org-3337	85	7	their	-PRON-	PRP$
en-wikipedia-org-3337	85	8	own	own	JJ
en-wikipedia-org-3337	85	9	situation	situation	NN
en-wikipedia-org-3337	85	10	by	by	IN
en-wikipedia-org-3337	85	11	breaking	break	VBG
en-wikipedia-org-3337	85	12	the	the	DT
en-wikipedia-org-3337	85	13	mutual	mutual	JJ
en-wikipedia-org-3337	85	14	cooperation	cooperation	NN
en-wikipedia-org-3337	85	15	,	,	,
en-wikipedia-org-3337	85	16	no	no	RB
en-wikipedia-org-3337	85	17	matter	matter	RB
en-wikipedia-org-3337	85	18	how	how	WRB
en-wikipedia-org-3337	85	19	the	the	DT
en-wikipedia-org-3337	85	20	other	other	JJ
en-wikipedia-org-3337	85	21	player	player	NN
en-wikipedia-org-3337	85	22	possibly	possibly	RB
en-wikipedia-org-3337	85	23	(	(	-LRB-
en-wikipedia-org-3337	85	24	or	or	CC
en-wikipedia-org-3337	85	25	certainly	certainly	RB
en-wikipedia-org-3337	85	26	)	)	-RRB-
en-wikipedia-org-3337	85	27	changes	change	VBZ
en-wikipedia-org-3337	85	28	their	-PRON-	PRP$
en-wikipedia-org-3337	85	29	decision	decision	NN
en-wikipedia-org-3337	85	30	.	.	.
en-wikipedia-org-3337	86	1	Network	network	NN
en-wikipedia-org-3337	86	2	traffic[edit	traffic[edit	NFP
en-wikipedia-org-3337	86	3	]	]	-RRB-
en-wikipedia-org-3337	86	4	See	see	VB
en-wikipedia-org-3337	86	5	also	also	RB
en-wikipedia-org-3337	86	6	:	:	:
en-wikipedia-org-3337	86	7	Braess	braess	NN
en-wikipedia-org-3337	86	8	's	's	POS
en-wikipedia-org-3337	86	9	paradox	paradox	NN
en-wikipedia-org-3337	86	10	Sample	Sample	NNP
en-wikipedia-org-3337	86	11	network	network	NN
en-wikipedia-org-3337	86	12	graph	graph	NN
en-wikipedia-org-3337	86	13	.	.	.
en-wikipedia-org-3337	87	1	Values	value	NNS
en-wikipedia-org-3337	87	2	on	on	IN
en-wikipedia-org-3337	87	3	edges	edge	NNS
en-wikipedia-org-3337	87	4	are	be	VBP
en-wikipedia-org-3337	87	5	the	the	DT
en-wikipedia-org-3337	87	6	travel	travel	NN
en-wikipedia-org-3337	87	7	time	time	NN
en-wikipedia-org-3337	87	8	experienced	experience	VBN
en-wikipedia-org-3337	87	9	by	by	IN
en-wikipedia-org-3337	87	10	a	a	DT
en-wikipedia-org-3337	87	11	'	'	``
en-wikipedia-org-3337	87	12	car	car	NN
en-wikipedia-org-3337	87	13	'	'	''
en-wikipedia-org-3337	87	14	traveling	travel	VBG
en-wikipedia-org-3337	87	15	down	down	IN
en-wikipedia-org-3337	87	16	that	that	DT
en-wikipedia-org-3337	87	17	edge	edge	NN
en-wikipedia-org-3337	87	18	.	.	.
en-wikipedia-org-3337	88	1	x	x	LS
en-wikipedia-org-3337	88	2	is	be	VBZ
en-wikipedia-org-3337	88	3	the	the	DT
en-wikipedia-org-3337	88	4	number	number	NN
en-wikipedia-org-3337	88	5	of	of	IN
en-wikipedia-org-3337	88	6	cars	car	NNS
en-wikipedia-org-3337	88	7	traveling	travel	VBG
en-wikipedia-org-3337	88	8	via	via	IN
en-wikipedia-org-3337	88	9	that	that	DT
en-wikipedia-org-3337	88	10	edge	edge	NN
en-wikipedia-org-3337	88	11	.	.	.
en-wikipedia-org-3337	89	1	An	an	DT
en-wikipedia-org-3337	89	2	application	application	NN
en-wikipedia-org-3337	89	3	of	of	IN
en-wikipedia-org-3337	89	4	Nash	Nash	NNP
en-wikipedia-org-3337	89	5	equilibria	equilibria	NN
en-wikipedia-org-3337	89	6	is	be	VBZ
en-wikipedia-org-3337	89	7	in	in	IN
en-wikipedia-org-3337	89	8	determining	determine	VBG
en-wikipedia-org-3337	89	9	the	the	DT
en-wikipedia-org-3337	89	10	expected	expect	VBN
en-wikipedia-org-3337	89	11	flow	flow	NN
en-wikipedia-org-3337	89	12	of	of	IN
en-wikipedia-org-3337	89	13	traffic	traffic	NN
en-wikipedia-org-3337	89	14	in	in	IN
en-wikipedia-org-3337	89	15	a	a	DT
en-wikipedia-org-3337	89	16	network	network	NN
en-wikipedia-org-3337	89	17	.	.	.
en-wikipedia-org-3337	90	1	Consider	consider	VB
en-wikipedia-org-3337	90	2	the	the	DT
en-wikipedia-org-3337	90	3	graph	graph	NN
en-wikipedia-org-3337	90	4	on	on	IN
en-wikipedia-org-3337	90	5	the	the	DT
en-wikipedia-org-3337	90	6	right	right	NN
en-wikipedia-org-3337	90	7	.	.	.
en-wikipedia-org-3337	91	1	If	if	IN
en-wikipedia-org-3337	91	2	we	-PRON-	PRP
en-wikipedia-org-3337	91	3	assume	assume	VBP
en-wikipedia-org-3337	91	4	that	that	IN
en-wikipedia-org-3337	91	5	there	there	EX
en-wikipedia-org-3337	91	6	are	be	VBP
en-wikipedia-org-3337	91	7	x	x	SYM
en-wikipedia-org-3337	91	8	"	"	``
en-wikipedia-org-3337	91	9	cars	car	NNS
en-wikipedia-org-3337	91	10	"	"	''
en-wikipedia-org-3337	91	11	traveling	travel	VBG
en-wikipedia-org-3337	91	12	from	from	IN
en-wikipedia-org-3337	91	13	A	a	NN
en-wikipedia-org-3337	91	14	to	to	IN
en-wikipedia-org-3337	91	15	D	d	NN
en-wikipedia-org-3337	91	16	,	,	,
en-wikipedia-org-3337	91	17	what	what	WP
en-wikipedia-org-3337	91	18	is	be	VBZ
en-wikipedia-org-3337	91	19	the	the	DT
en-wikipedia-org-3337	91	20	expected	expected	JJ
en-wikipedia-org-3337	91	21	distribution	distribution	NN
en-wikipedia-org-3337	91	22	of	of	IN
en-wikipedia-org-3337	91	23	traffic	traffic	NN
en-wikipedia-org-3337	91	24	in	in	IN
en-wikipedia-org-3337	91	25	the	the	DT
en-wikipedia-org-3337	91	26	network	network	NN
en-wikipedia-org-3337	91	27	?	?	.
en-wikipedia-org-3337	92	1	This	this	DT
en-wikipedia-org-3337	92	2	situation	situation	NN
en-wikipedia-org-3337	92	3	can	can	MD
en-wikipedia-org-3337	92	4	be	be	VB
en-wikipedia-org-3337	92	5	modeled	model	VBN
en-wikipedia-org-3337	92	6	as	as	IN
en-wikipedia-org-3337	92	7	a	a	DT
en-wikipedia-org-3337	92	8	"	"	``
en-wikipedia-org-3337	92	9	game	game	NN
en-wikipedia-org-3337	92	10	"	"	''
en-wikipedia-org-3337	92	11	where	where	WRB
en-wikipedia-org-3337	92	12	every	every	DT
en-wikipedia-org-3337	92	13	traveler	traveler	NN
en-wikipedia-org-3337	92	14	has	have	VBZ
en-wikipedia-org-3337	92	15	a	a	DT
en-wikipedia-org-3337	92	16	choice	choice	NN
en-wikipedia-org-3337	92	17	of	of	IN
en-wikipedia-org-3337	92	18	3	3	CD
en-wikipedia-org-3337	92	19	strategies	strategy	NNS
en-wikipedia-org-3337	92	20	,	,	,
en-wikipedia-org-3337	92	21	where	where	WRB
en-wikipedia-org-3337	92	22	each	each	DT
en-wikipedia-org-3337	92	23	strategy	strategy	NN
en-wikipedia-org-3337	92	24	is	be	VBZ
en-wikipedia-org-3337	92	25	a	a	DT
en-wikipedia-org-3337	92	26	route	route	NN
en-wikipedia-org-3337	92	27	from	from	IN
en-wikipedia-org-3337	92	28	A	a	NN
en-wikipedia-org-3337	92	29	to	to	IN
en-wikipedia-org-3337	92	30	D	d	NN
en-wikipedia-org-3337	92	31	(	(	-LRB-
en-wikipedia-org-3337	92	32	either	either	CC
en-wikipedia-org-3337	92	33	ABD	ABD	NNP
en-wikipedia-org-3337	92	34	,	,	,
en-wikipedia-org-3337	92	35	ABCD	ABCD	NNP
en-wikipedia-org-3337	92	36	,	,	,
en-wikipedia-org-3337	92	37	or	or	CC
en-wikipedia-org-3337	92	38	ACD	ACD	NNP
en-wikipedia-org-3337	92	39	)	)	-RRB-
en-wikipedia-org-3337	92	40	.	.	.
en-wikipedia-org-3337	93	1	The	the	DT
en-wikipedia-org-3337	93	2	"	"	``
en-wikipedia-org-3337	93	3	payoff	payoff	NN
en-wikipedia-org-3337	93	4	"	"	''
en-wikipedia-org-3337	93	5	of	of	IN
en-wikipedia-org-3337	93	6	each	each	DT
en-wikipedia-org-3337	93	7	strategy	strategy	NN
en-wikipedia-org-3337	93	8	is	be	VBZ
en-wikipedia-org-3337	93	9	the	the	DT
en-wikipedia-org-3337	93	10	travel	travel	NN
en-wikipedia-org-3337	93	11	time	time	NN
en-wikipedia-org-3337	93	12	of	of	IN
en-wikipedia-org-3337	93	13	each	each	DT
en-wikipedia-org-3337	93	14	route	route	NN
en-wikipedia-org-3337	93	15	.	.	.
en-wikipedia-org-3337	94	1	In	in	IN
en-wikipedia-org-3337	94	2	the	the	DT
en-wikipedia-org-3337	94	3	graph	graph	NN
en-wikipedia-org-3337	94	4	on	on	IN
en-wikipedia-org-3337	94	5	the	the	DT
en-wikipedia-org-3337	94	6	right	right	NN
en-wikipedia-org-3337	94	7	,	,	,
en-wikipedia-org-3337	94	8	a	a	DT
en-wikipedia-org-3337	94	9	car	car	NN
en-wikipedia-org-3337	94	10	travelling	travel	VBG
en-wikipedia-org-3337	94	11	via	via	IN
en-wikipedia-org-3337	94	12	ABD	ABD	NNP
en-wikipedia-org-3337	94	13	experiences	experience	NNS
en-wikipedia-org-3337	94	14	travel	travel	VBP
en-wikipedia-org-3337	94	15	time	time	NN
en-wikipedia-org-3337	94	16	of	of	IN
en-wikipedia-org-3337	94	17	(	(	-LRB-
en-wikipedia-org-3337	94	18	1+x/100)+2	1+x/100)+2	CD
en-wikipedia-org-3337	94	19	,	,	,
en-wikipedia-org-3337	94	20	where	where	WRB
en-wikipedia-org-3337	94	21	x	x	NNP
en-wikipedia-org-3337	94	22	is	be	VBZ
en-wikipedia-org-3337	94	23	the	the	DT
en-wikipedia-org-3337	94	24	number	number	NN
en-wikipedia-org-3337	94	25	of	of	IN
en-wikipedia-org-3337	94	26	cars	car	NNS
en-wikipedia-org-3337	94	27	traveling	travel	VBG
en-wikipedia-org-3337	94	28	on	on	IN
en-wikipedia-org-3337	94	29	edge	edge	NN
en-wikipedia-org-3337	94	30	AB	AB	NNP
en-wikipedia-org-3337	94	31	.	.	.
en-wikipedia-org-3337	95	1	Thus	thus	RB
en-wikipedia-org-3337	95	2	,	,	,
en-wikipedia-org-3337	95	3	payoffs	payoff	NNS
en-wikipedia-org-3337	95	4	for	for	IN
en-wikipedia-org-3337	95	5	any	any	DT
en-wikipedia-org-3337	95	6	given	give	VBN
en-wikipedia-org-3337	95	7	strategy	strategy	NN
en-wikipedia-org-3337	95	8	depend	depend	VB
en-wikipedia-org-3337	95	9	on	on	IN
en-wikipedia-org-3337	95	10	the	the	DT
en-wikipedia-org-3337	95	11	choices	choice	NNS
en-wikipedia-org-3337	95	12	of	of	IN
en-wikipedia-org-3337	95	13	the	the	DT
en-wikipedia-org-3337	95	14	other	other	JJ
en-wikipedia-org-3337	95	15	players	player	NNS
en-wikipedia-org-3337	95	16	,	,	,
en-wikipedia-org-3337	95	17	as	as	IN
en-wikipedia-org-3337	95	18	is	be	VBZ
en-wikipedia-org-3337	95	19	usual	usual	JJ
en-wikipedia-org-3337	95	20	.	.	.
en-wikipedia-org-3337	96	1	However	however	RB
en-wikipedia-org-3337	96	2	,	,	,
en-wikipedia-org-3337	96	3	the	the	DT
en-wikipedia-org-3337	96	4	goal	goal	NN
en-wikipedia-org-3337	96	5	,	,	,
en-wikipedia-org-3337	96	6	in	in	IN
en-wikipedia-org-3337	96	7	this	this	DT
en-wikipedia-org-3337	96	8	case	case	NN
en-wikipedia-org-3337	96	9	,	,	,
en-wikipedia-org-3337	96	10	is	be	VBZ
en-wikipedia-org-3337	96	11	to	to	TO
en-wikipedia-org-3337	96	12	minimize	minimize	VB
en-wikipedia-org-3337	96	13	travel	travel	NN
en-wikipedia-org-3337	96	14	time	time	NN
en-wikipedia-org-3337	96	15	,	,	,
en-wikipedia-org-3337	96	16	not	not	RB
en-wikipedia-org-3337	96	17	maximize	maximize	VB
en-wikipedia-org-3337	96	18	it	-PRON-	PRP
en-wikipedia-org-3337	96	19	.	.	.
en-wikipedia-org-3337	97	1	Equilibrium	equilibrium	NN
en-wikipedia-org-3337	97	2	will	will	MD
en-wikipedia-org-3337	97	3	occur	occur	VB
en-wikipedia-org-3337	97	4	when	when	WRB
en-wikipedia-org-3337	97	5	the	the	DT
en-wikipedia-org-3337	97	6	time	time	NN
en-wikipedia-org-3337	97	7	on	on	IN
en-wikipedia-org-3337	97	8	all	all	DT
en-wikipedia-org-3337	97	9	paths	path	NNS
en-wikipedia-org-3337	97	10	is	be	VBZ
en-wikipedia-org-3337	97	11	exactly	exactly	RB
en-wikipedia-org-3337	97	12	the	the	DT
en-wikipedia-org-3337	97	13	same	same	JJ
en-wikipedia-org-3337	97	14	.	.	.
en-wikipedia-org-3337	98	1	When	when	WRB
en-wikipedia-org-3337	98	2	that	that	DT
en-wikipedia-org-3337	98	3	happens	happen	VBZ
en-wikipedia-org-3337	98	4	,	,	,
en-wikipedia-org-3337	98	5	no	no	DT
en-wikipedia-org-3337	98	6	single	single	JJ
en-wikipedia-org-3337	98	7	driver	driver	NN
en-wikipedia-org-3337	98	8	has	have	VBZ
en-wikipedia-org-3337	98	9	any	any	DT
en-wikipedia-org-3337	98	10	incentive	incentive	NN
en-wikipedia-org-3337	98	11	to	to	TO
en-wikipedia-org-3337	98	12	switch	switch	VB
en-wikipedia-org-3337	98	13	routes	route	NNS
en-wikipedia-org-3337	98	14	,	,	,
en-wikipedia-org-3337	98	15	since	since	IN
en-wikipedia-org-3337	98	16	it	-PRON-	PRP
en-wikipedia-org-3337	98	17	can	can	MD
en-wikipedia-org-3337	98	18	only	only	RB
en-wikipedia-org-3337	98	19	add	add	VB
en-wikipedia-org-3337	98	20	to	to	IN
en-wikipedia-org-3337	98	21	their	-PRON-	PRP$
en-wikipedia-org-3337	98	22	travel	travel	NN
en-wikipedia-org-3337	98	23	time	time	NN
en-wikipedia-org-3337	98	24	.	.	.
en-wikipedia-org-3337	99	1	For	for	IN
en-wikipedia-org-3337	99	2	the	the	DT
en-wikipedia-org-3337	99	3	graph	graph	NN
en-wikipedia-org-3337	99	4	on	on	IN
en-wikipedia-org-3337	99	5	the	the	DT
en-wikipedia-org-3337	99	6	right	right	NN
en-wikipedia-org-3337	99	7	,	,	,
en-wikipedia-org-3337	99	8	if	if	IN
en-wikipedia-org-3337	99	9	,	,	,
en-wikipedia-org-3337	99	10	for	for	IN
en-wikipedia-org-3337	99	11	example	example	NN
en-wikipedia-org-3337	99	12	,	,	,
en-wikipedia-org-3337	99	13	100	100	CD
en-wikipedia-org-3337	99	14	cars	car	NNS
en-wikipedia-org-3337	99	15	are	be	VBP
en-wikipedia-org-3337	99	16	travelling	travel	VBG
en-wikipedia-org-3337	99	17	from	from	IN
en-wikipedia-org-3337	99	18	A	a	NN
en-wikipedia-org-3337	99	19	to	to	IN
en-wikipedia-org-3337	99	20	D	d	NN
en-wikipedia-org-3337	99	21	,	,	,
en-wikipedia-org-3337	99	22	then	then	RB
en-wikipedia-org-3337	99	23	equilibrium	equilibrium	NN
en-wikipedia-org-3337	99	24	will	will	MD
en-wikipedia-org-3337	99	25	occur	occur	VB
en-wikipedia-org-3337	99	26	when	when	WRB
en-wikipedia-org-3337	99	27	25	25	CD
en-wikipedia-org-3337	99	28	drivers	driver	NNS
en-wikipedia-org-3337	99	29	travel	travel	VBP
en-wikipedia-org-3337	99	30	via	via	IN
en-wikipedia-org-3337	99	31	ABD	ABD	NNP
en-wikipedia-org-3337	99	32	,	,	,
en-wikipedia-org-3337	99	33	50	50	CD
en-wikipedia-org-3337	99	34	via	via	IN
en-wikipedia-org-3337	99	35	ABCD	ABCD	NNP
en-wikipedia-org-3337	99	36	,	,	,
en-wikipedia-org-3337	99	37	and	and	CC
en-wikipedia-org-3337	99	38	25	25	CD
en-wikipedia-org-3337	99	39	via	via	IN
en-wikipedia-org-3337	99	40	ACD	acd	NN
en-wikipedia-org-3337	99	41	.	.	.
en-wikipedia-org-3337	100	1	Every	every	DT
en-wikipedia-org-3337	100	2	driver	driver	NN
en-wikipedia-org-3337	100	3	now	now	RB
en-wikipedia-org-3337	100	4	has	have	VBZ
en-wikipedia-org-3337	100	5	a	a	DT
en-wikipedia-org-3337	100	6	total	total	JJ
en-wikipedia-org-3337	100	7	travel	travel	NN
en-wikipedia-org-3337	100	8	time	time	NN
en-wikipedia-org-3337	100	9	of	of	IN
en-wikipedia-org-3337	100	10	3.75	3.75	CD
en-wikipedia-org-3337	100	11	(	(	-LRB-
en-wikipedia-org-3337	100	12	to	to	TO
en-wikipedia-org-3337	100	13	see	see	VB
en-wikipedia-org-3337	100	14	this	this	DT
en-wikipedia-org-3337	100	15	,	,	,
en-wikipedia-org-3337	100	16	note	note	VB
en-wikipedia-org-3337	100	17	that	that	IN
en-wikipedia-org-3337	100	18	a	a	DT
en-wikipedia-org-3337	100	19	total	total	NN
en-wikipedia-org-3337	100	20	of	of	IN
en-wikipedia-org-3337	100	21	75	75	CD
en-wikipedia-org-3337	100	22	cars	car	NNS
en-wikipedia-org-3337	100	23	take	take	VBP
en-wikipedia-org-3337	100	24	the	the	DT
en-wikipedia-org-3337	100	25	AB	AB	NNP
en-wikipedia-org-3337	100	26	edge	edge	NN
en-wikipedia-org-3337	100	27	,	,	,
en-wikipedia-org-3337	100	28	and	and	CC
en-wikipedia-org-3337	100	29	likewise	likewise	RB
en-wikipedia-org-3337	100	30	,	,	,
en-wikipedia-org-3337	100	31	75	75	CD
en-wikipedia-org-3337	100	32	cars	car	NNS
en-wikipedia-org-3337	100	33	take	take	VBP
en-wikipedia-org-3337	100	34	the	the	DT
en-wikipedia-org-3337	100	35	CD	cd	NN
en-wikipedia-org-3337	100	36	edge	edge	NN
en-wikipedia-org-3337	100	37	)	)	-RRB-
en-wikipedia-org-3337	100	38	.	.	.
en-wikipedia-org-3337	101	1	Notice	notice	VB
en-wikipedia-org-3337	101	2	that	that	IN
en-wikipedia-org-3337	101	3	this	this	DT
en-wikipedia-org-3337	101	4	distribution	distribution	NN
en-wikipedia-org-3337	101	5	is	be	VBZ
en-wikipedia-org-3337	101	6	not	not	RB
en-wikipedia-org-3337	101	7	,	,	,
en-wikipedia-org-3337	101	8	actually	actually	RB
en-wikipedia-org-3337	101	9	,	,	,
en-wikipedia-org-3337	101	10	socially	socially	RB
en-wikipedia-org-3337	101	11	optimal	optimal	JJ
en-wikipedia-org-3337	101	12	.	.	.
en-wikipedia-org-3337	102	1	If	if	IN
en-wikipedia-org-3337	102	2	the	the	DT
en-wikipedia-org-3337	102	3	100	100	CD
en-wikipedia-org-3337	102	4	cars	car	NNS
en-wikipedia-org-3337	102	5	agreed	agree	VBD
en-wikipedia-org-3337	102	6	that	that	IN
en-wikipedia-org-3337	102	7	50	50	CD
en-wikipedia-org-3337	102	8	travel	travel	NN
en-wikipedia-org-3337	102	9	via	via	IN
en-wikipedia-org-3337	102	10	ABD	ABD	NNP
en-wikipedia-org-3337	102	11	and	and	CC
en-wikipedia-org-3337	102	12	the	the	DT
en-wikipedia-org-3337	102	13	other	other	JJ
en-wikipedia-org-3337	102	14	50	50	CD
en-wikipedia-org-3337	102	15	through	through	IN
en-wikipedia-org-3337	102	16	ACD	acd	NN
en-wikipedia-org-3337	102	17	,	,	,
en-wikipedia-org-3337	102	18	then	then	RB
en-wikipedia-org-3337	102	19	travel	travel	NN
en-wikipedia-org-3337	102	20	time	time	NN
en-wikipedia-org-3337	102	21	for	for	IN
en-wikipedia-org-3337	102	22	any	any	DT
en-wikipedia-org-3337	102	23	single	single	JJ
en-wikipedia-org-3337	102	24	car	car	NN
en-wikipedia-org-3337	102	25	would	would	MD
en-wikipedia-org-3337	102	26	actually	actually	RB
en-wikipedia-org-3337	102	27	be	be	VB
en-wikipedia-org-3337	102	28	3.5	3.5	CD
en-wikipedia-org-3337	102	29	,	,	,
en-wikipedia-org-3337	102	30	which	which	WDT
en-wikipedia-org-3337	102	31	is	be	VBZ
en-wikipedia-org-3337	102	32	less	less	JJR
en-wikipedia-org-3337	102	33	than	than	IN
en-wikipedia-org-3337	102	34	3.75	3.75	CD
en-wikipedia-org-3337	102	35	.	.	.
en-wikipedia-org-3337	103	1	This	this	DT
en-wikipedia-org-3337	103	2	is	be	VBZ
en-wikipedia-org-3337	103	3	also	also	RB
en-wikipedia-org-3337	103	4	the	the	DT
en-wikipedia-org-3337	103	5	Nash	Nash	NNP
en-wikipedia-org-3337	103	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	103	7	if	if	IN
en-wikipedia-org-3337	103	8	the	the	DT
en-wikipedia-org-3337	103	9	path	path	NN
en-wikipedia-org-3337	103	10	between	between	IN
en-wikipedia-org-3337	103	11	B	B	NNP
en-wikipedia-org-3337	103	12	and	and	CC
en-wikipedia-org-3337	103	13	C	C	NNP
en-wikipedia-org-3337	103	14	is	be	VBZ
en-wikipedia-org-3337	103	15	removed	remove	VBN
en-wikipedia-org-3337	103	16	,	,	,
en-wikipedia-org-3337	103	17	which	which	WDT
en-wikipedia-org-3337	103	18	means	mean	VBZ
en-wikipedia-org-3337	103	19	that	that	IN
en-wikipedia-org-3337	103	20	adding	add	VBG
en-wikipedia-org-3337	103	21	another	another	DT
en-wikipedia-org-3337	103	22	possible	possible	JJ
en-wikipedia-org-3337	103	23	route	route	NN
en-wikipedia-org-3337	103	24	can	can	MD
en-wikipedia-org-3337	103	25	decrease	decrease	VB
en-wikipedia-org-3337	103	26	the	the	DT
en-wikipedia-org-3337	103	27	efficiency	efficiency	NN
en-wikipedia-org-3337	103	28	of	of	IN
en-wikipedia-org-3337	103	29	the	the	DT
en-wikipedia-org-3337	103	30	system	system	NN
en-wikipedia-org-3337	103	31	,	,	,
en-wikipedia-org-3337	103	32	a	a	DT
en-wikipedia-org-3337	103	33	phenomenon	phenomenon	NN
en-wikipedia-org-3337	103	34	known	know	VBN
en-wikipedia-org-3337	103	35	as	as	IN
en-wikipedia-org-3337	103	36	Braess	Braess	NNP
en-wikipedia-org-3337	103	37	's	's	POS
en-wikipedia-org-3337	103	38	paradox	paradox	NN
en-wikipedia-org-3337	103	39	.	.	.
en-wikipedia-org-3337	104	1	Competition	competition	NN
en-wikipedia-org-3337	104	2	game[edit	game[edit	NFP
en-wikipedia-org-3337	104	3	]	]	-RRB-
en-wikipedia-org-3337	104	4	A	a	DT
en-wikipedia-org-3337	104	5	competition	competition	NN
en-wikipedia-org-3337	104	6	game	game	NN
en-wikipedia-org-3337	104	7	Player	Player	NNP
en-wikipedia-org-3337	104	8	2	2	CD
en-wikipedia-org-3337	104	9	Player	Player	NNP
en-wikipedia-org-3337	104	10	1	1	CD
en-wikipedia-org-3337	104	11	Choose	Choose	NNP
en-wikipedia-org-3337	104	12	'	'	CD
en-wikipedia-org-3337	104	13	0	0	CD
en-wikipedia-org-3337	104	14	'	'	''
en-wikipedia-org-3337	104	15	Choose	choose	VB
en-wikipedia-org-3337	104	16	'	'	``
en-wikipedia-org-3337	104	17	1	1	CD
en-wikipedia-org-3337	104	18	'	'	''
en-wikipedia-org-3337	104	19	Choose	choose	VB
en-wikipedia-org-3337	104	20	'	'	''
en-wikipedia-org-3337	104	21	2	2	CD
en-wikipedia-org-3337	104	22	'	'	''
en-wikipedia-org-3337	104	23	Choose	choose	VB
en-wikipedia-org-3337	104	24	'	'	CD
en-wikipedia-org-3337	104	25	3	3	CD
en-wikipedia-org-3337	104	26	'	'	''
en-wikipedia-org-3337	104	27	Choose	choose	VB
en-wikipedia-org-3337	104	28	'	'	CD
en-wikipedia-org-3337	104	29	0	0	CD
en-wikipedia-org-3337	104	30	'	'	CD
en-wikipedia-org-3337	104	31	0	0	CD
en-wikipedia-org-3337	104	32	,	,	,
en-wikipedia-org-3337	104	33	0	0	CD
en-wikipedia-org-3337	104	34	2	2	CD
en-wikipedia-org-3337	104	35	,	,	,
en-wikipedia-org-3337	104	36	−2	−2	NNP
en-wikipedia-org-3337	104	37	2	2	CD
en-wikipedia-org-3337	104	38	,	,	,
en-wikipedia-org-3337	104	39	−2	−2	NNP
en-wikipedia-org-3337	104	40	2	2	CD
en-wikipedia-org-3337	104	41	,	,	,
en-wikipedia-org-3337	104	42	−2	−2	NNP
en-wikipedia-org-3337	104	43	Choose	Choose	NNP
en-wikipedia-org-3337	104	44	'	'	POS
en-wikipedia-org-3337	104	45	1	1	CD
en-wikipedia-org-3337	104	46	'	'	CD
en-wikipedia-org-3337	104	47	−2	−2	NNP
en-wikipedia-org-3337	104	48	,	,	,
en-wikipedia-org-3337	104	49	2	2	CD
en-wikipedia-org-3337	104	50	1	1	CD
en-wikipedia-org-3337	104	51	,	,	,
en-wikipedia-org-3337	104	52	1	1	CD
en-wikipedia-org-3337	104	53	3	3	CD
en-wikipedia-org-3337	104	54	,	,	,
en-wikipedia-org-3337	104	55	−1	−1	NNP
en-wikipedia-org-3337	104	56	3	3	CD
en-wikipedia-org-3337	104	57	,	,	,
en-wikipedia-org-3337	104	58	−1	−1	NNP
en-wikipedia-org-3337	104	59	Choose	Choose	NNP
en-wikipedia-org-3337	104	60	'	'	POS
en-wikipedia-org-3337	104	61	2	2	CD
en-wikipedia-org-3337	104	62	'	'	CD
en-wikipedia-org-3337	104	63	−2	−2	NNP
en-wikipedia-org-3337	104	64	,	,	,
en-wikipedia-org-3337	104	65	2	2	CD
en-wikipedia-org-3337	104	66	−1	−1	NNP
en-wikipedia-org-3337	104	67	,	,	,
en-wikipedia-org-3337	104	68	3	3	CD
en-wikipedia-org-3337	104	69	2	2	CD
en-wikipedia-org-3337	104	70	,	,	,
en-wikipedia-org-3337	104	71	2	2	CD
en-wikipedia-org-3337	104	72	4	4	CD
en-wikipedia-org-3337	104	73	,	,	,
en-wikipedia-org-3337	104	74	0	0	NFP
en-wikipedia-org-3337	104	75	Choose	Choose	NNP
en-wikipedia-org-3337	104	76	'	'	CD
en-wikipedia-org-3337	104	77	3	3	CD
en-wikipedia-org-3337	104	78	'	'	POS
en-wikipedia-org-3337	104	79	−2	−2	NNP
en-wikipedia-org-3337	104	80	,	,	,
en-wikipedia-org-3337	104	81	2	2	CD
en-wikipedia-org-3337	104	82	−1	−1	NNP
en-wikipedia-org-3337	104	83	,	,	,
en-wikipedia-org-3337	104	84	3	3	CD
en-wikipedia-org-3337	104	85	0	0	CD
en-wikipedia-org-3337	104	86	,	,	,
en-wikipedia-org-3337	104	87	4	4	CD
en-wikipedia-org-3337	104	88	3	3	CD
en-wikipedia-org-3337	104	89	,	,	,
en-wikipedia-org-3337	104	90	3	3	CD
en-wikipedia-org-3337	104	91	This	this	DT
en-wikipedia-org-3337	104	92	can	can	MD
en-wikipedia-org-3337	104	93	be	be	VB
en-wikipedia-org-3337	104	94	illustrated	illustrate	VBN
en-wikipedia-org-3337	104	95	by	by	IN
en-wikipedia-org-3337	104	96	a	a	DT
en-wikipedia-org-3337	104	97	two	two	CD
en-wikipedia-org-3337	104	98	-	-	HYPH
en-wikipedia-org-3337	104	99	player	player	NN
en-wikipedia-org-3337	104	100	game	game	NN
en-wikipedia-org-3337	104	101	in	in	IN
en-wikipedia-org-3337	104	102	which	which	WDT
en-wikipedia-org-3337	104	103	both	both	DT
en-wikipedia-org-3337	104	104	players	player	NNS
en-wikipedia-org-3337	104	105	simultaneously	simultaneously	RB
en-wikipedia-org-3337	104	106	choose	choose	VBP
en-wikipedia-org-3337	104	107	an	an	DT
en-wikipedia-org-3337	104	108	integer	integer	NN
en-wikipedia-org-3337	104	109	from	from	IN
en-wikipedia-org-3337	104	110	0	0	CD
en-wikipedia-org-3337	104	111	to	to	IN
en-wikipedia-org-3337	104	112	3	3	CD
en-wikipedia-org-3337	104	113	and	and	CC
en-wikipedia-org-3337	104	114	they	-PRON-	PRP
en-wikipedia-org-3337	104	115	both	both	DT
en-wikipedia-org-3337	104	116	win	win	VBP
en-wikipedia-org-3337	104	117	the	the	DT
en-wikipedia-org-3337	104	118	smaller	small	JJR
en-wikipedia-org-3337	104	119	of	of	IN
en-wikipedia-org-3337	104	120	the	the	DT
en-wikipedia-org-3337	104	121	two	two	CD
en-wikipedia-org-3337	104	122	numbers	number	NNS
en-wikipedia-org-3337	104	123	in	in	IN
en-wikipedia-org-3337	104	124	points	point	NNS
en-wikipedia-org-3337	104	125	.	.	.
en-wikipedia-org-3337	105	1	In	in	IN
en-wikipedia-org-3337	105	2	addition	addition	NN
en-wikipedia-org-3337	105	3	,	,	,
en-wikipedia-org-3337	105	4	if	if	IN
en-wikipedia-org-3337	105	5	one	one	CD
en-wikipedia-org-3337	105	6	player	player	NN
en-wikipedia-org-3337	105	7	chooses	choose	VBZ
en-wikipedia-org-3337	105	8	a	a	DT
en-wikipedia-org-3337	105	9	larger	large	JJR
en-wikipedia-org-3337	105	10	number	number	NN
en-wikipedia-org-3337	105	11	than	than	IN
en-wikipedia-org-3337	105	12	the	the	DT
en-wikipedia-org-3337	105	13	other	other	JJ
en-wikipedia-org-3337	105	14	,	,	,
en-wikipedia-org-3337	105	15	then	then	RB
en-wikipedia-org-3337	105	16	they	-PRON-	PRP
en-wikipedia-org-3337	105	17	have	have	VBP
en-wikipedia-org-3337	105	18	to	to	TO
en-wikipedia-org-3337	105	19	give	give	VB
en-wikipedia-org-3337	105	20	up	up	RP
en-wikipedia-org-3337	105	21	two	two	CD
en-wikipedia-org-3337	105	22	points	point	NNS
en-wikipedia-org-3337	105	23	to	to	IN
en-wikipedia-org-3337	105	24	the	the	DT
en-wikipedia-org-3337	105	25	other	other	JJ
en-wikipedia-org-3337	105	26	.	.	.
en-wikipedia-org-3337	106	1	This	this	DT
en-wikipedia-org-3337	106	2	game	game	NN
en-wikipedia-org-3337	106	3	has	have	VBZ
en-wikipedia-org-3337	106	4	a	a	DT
en-wikipedia-org-3337	106	5	unique	unique	JJ
en-wikipedia-org-3337	106	6	pure	pure	JJ
en-wikipedia-org-3337	106	7	-	-	HYPH
en-wikipedia-org-3337	106	8	strategy	strategy	NN
en-wikipedia-org-3337	106	9	Nash	Nash	NNP
en-wikipedia-org-3337	106	10	equilibrium	equilibrium	NN
en-wikipedia-org-3337	106	11	:	:	:
en-wikipedia-org-3337	106	12	both	both	DT
en-wikipedia-org-3337	106	13	players	player	NNS
en-wikipedia-org-3337	106	14	choosing	choose	VBG
en-wikipedia-org-3337	106	15	0	0	CD
en-wikipedia-org-3337	106	16	(	(	-LRB-
en-wikipedia-org-3337	106	17	highlighted	highlight	VBN
en-wikipedia-org-3337	106	18	in	in	IN
en-wikipedia-org-3337	106	19	light	light	JJ
en-wikipedia-org-3337	106	20	red	red	NN
en-wikipedia-org-3337	106	21	)	)	-RRB-
en-wikipedia-org-3337	106	22	.	.	.
en-wikipedia-org-3337	107	1	Any	any	DT
en-wikipedia-org-3337	107	2	other	other	JJ
en-wikipedia-org-3337	107	3	strategy	strategy	NN
en-wikipedia-org-3337	107	4	can	can	MD
en-wikipedia-org-3337	107	5	be	be	VB
en-wikipedia-org-3337	107	6	improved	improve	VBN
en-wikipedia-org-3337	107	7	by	by	IN
en-wikipedia-org-3337	107	8	a	a	DT
en-wikipedia-org-3337	107	9	player	player	NN
en-wikipedia-org-3337	107	10	switching	switch	VBG
en-wikipedia-org-3337	107	11	their	-PRON-	PRP$
en-wikipedia-org-3337	107	12	number	number	NN
en-wikipedia-org-3337	107	13	to	to	IN
en-wikipedia-org-3337	107	14	one	one	CD
en-wikipedia-org-3337	107	15	less	less	JJR
en-wikipedia-org-3337	107	16	than	than	IN
en-wikipedia-org-3337	107	17	that	that	DT
en-wikipedia-org-3337	107	18	of	of	IN
en-wikipedia-org-3337	107	19	the	the	DT
en-wikipedia-org-3337	107	20	other	other	JJ
en-wikipedia-org-3337	107	21	player	player	NN
en-wikipedia-org-3337	107	22	.	.	.
en-wikipedia-org-3337	108	1	In	in	IN
en-wikipedia-org-3337	108	2	the	the	DT
en-wikipedia-org-3337	108	3	adjacent	adjacent	JJ
en-wikipedia-org-3337	108	4	table	table	NN
en-wikipedia-org-3337	108	5	,	,	,
en-wikipedia-org-3337	108	6	if	if	IN
en-wikipedia-org-3337	108	7	the	the	DT
en-wikipedia-org-3337	108	8	game	game	NN
en-wikipedia-org-3337	108	9	begins	begin	VBZ
en-wikipedia-org-3337	108	10	at	at	IN
en-wikipedia-org-3337	108	11	the	the	DT
en-wikipedia-org-3337	108	12	green	green	NNP
en-wikipedia-org-3337	108	13	square	square	NN
en-wikipedia-org-3337	108	14	,	,	,
en-wikipedia-org-3337	108	15	it	-PRON-	PRP
en-wikipedia-org-3337	108	16	is	be	VBZ
en-wikipedia-org-3337	108	17	in	in	IN
en-wikipedia-org-3337	108	18	player	player	NN
en-wikipedia-org-3337	108	19	1	1	CD
en-wikipedia-org-3337	108	20	's	's	POS
en-wikipedia-org-3337	108	21	interest	interest	NN
en-wikipedia-org-3337	108	22	to	to	TO
en-wikipedia-org-3337	108	23	move	move	VB
en-wikipedia-org-3337	108	24	to	to	IN
en-wikipedia-org-3337	108	25	the	the	DT
en-wikipedia-org-3337	108	26	purple	purple	JJ
en-wikipedia-org-3337	108	27	square	square	NN
en-wikipedia-org-3337	108	28	and	and	CC
en-wikipedia-org-3337	108	29	it	-PRON-	PRP
en-wikipedia-org-3337	108	30	is	be	VBZ
en-wikipedia-org-3337	108	31	in	in	IN
en-wikipedia-org-3337	108	32	player	player	NN
en-wikipedia-org-3337	108	33	2	2	CD
en-wikipedia-org-3337	108	34	's	's	POS
en-wikipedia-org-3337	108	35	interest	interest	NN
en-wikipedia-org-3337	108	36	to	to	TO
en-wikipedia-org-3337	108	37	move	move	VB
en-wikipedia-org-3337	108	38	to	to	IN
en-wikipedia-org-3337	108	39	the	the	DT
en-wikipedia-org-3337	108	40	blue	blue	JJ
en-wikipedia-org-3337	108	41	square	square	NN
en-wikipedia-org-3337	108	42	.	.	.
en-wikipedia-org-3337	109	1	Although	although	IN
en-wikipedia-org-3337	109	2	it	-PRON-	PRP
en-wikipedia-org-3337	109	3	would	would	MD
en-wikipedia-org-3337	109	4	not	not	RB
en-wikipedia-org-3337	109	5	fit	fit	VB
en-wikipedia-org-3337	109	6	the	the	DT
en-wikipedia-org-3337	109	7	definition	definition	NN
en-wikipedia-org-3337	109	8	of	of	IN
en-wikipedia-org-3337	109	9	a	a	DT
en-wikipedia-org-3337	109	10	competition	competition	NN
en-wikipedia-org-3337	109	11	game	game	NN
en-wikipedia-org-3337	109	12	,	,	,
en-wikipedia-org-3337	109	13	if	if	IN
en-wikipedia-org-3337	109	14	the	the	DT
en-wikipedia-org-3337	109	15	game	game	NN
en-wikipedia-org-3337	109	16	is	be	VBZ
en-wikipedia-org-3337	109	17	modified	modify	VBN
en-wikipedia-org-3337	109	18	so	so	IN
en-wikipedia-org-3337	109	19	that	that	IN
en-wikipedia-org-3337	109	20	the	the	DT
en-wikipedia-org-3337	109	21	two	two	CD
en-wikipedia-org-3337	109	22	players	player	NNS
en-wikipedia-org-3337	109	23	win	win	VBP
en-wikipedia-org-3337	109	24	the	the	DT
en-wikipedia-org-3337	109	25	named	name	VBN
en-wikipedia-org-3337	109	26	amount	amount	NN
en-wikipedia-org-3337	109	27	if	if	IN
en-wikipedia-org-3337	109	28	they	-PRON-	PRP
en-wikipedia-org-3337	109	29	both	both	DT
en-wikipedia-org-3337	109	30	choose	choose	VBP
en-wikipedia-org-3337	109	31	the	the	DT
en-wikipedia-org-3337	109	32	same	same	JJ
en-wikipedia-org-3337	109	33	number	number	NN
en-wikipedia-org-3337	109	34	,	,	,
en-wikipedia-org-3337	109	35	and	and	CC
en-wikipedia-org-3337	109	36	otherwise	otherwise	RB
en-wikipedia-org-3337	109	37	win	win	VB
en-wikipedia-org-3337	109	38	nothing	nothing	NN
en-wikipedia-org-3337	109	39	,	,	,
en-wikipedia-org-3337	109	40	then	then	RB
en-wikipedia-org-3337	109	41	there	there	EX
en-wikipedia-org-3337	109	42	are	be	VBP
en-wikipedia-org-3337	109	43	4	4	CD
en-wikipedia-org-3337	109	44	Nash	Nash	NNP
en-wikipedia-org-3337	109	45	equilibria	equilibrium	NNS
en-wikipedia-org-3337	109	46	:	:	:
en-wikipedia-org-3337	109	47	(	(	-LRB-
en-wikipedia-org-3337	109	48	0,0	0,0	NFP
en-wikipedia-org-3337	109	49	)	)	-RRB-
en-wikipedia-org-3337	109	50	,	,	,
en-wikipedia-org-3337	109	51	(	(	-LRB-
en-wikipedia-org-3337	109	52	1,1	1,1	CD
en-wikipedia-org-3337	109	53	)	)	-RRB-
en-wikipedia-org-3337	109	54	,	,	,
en-wikipedia-org-3337	109	55	(	(	-LRB-
en-wikipedia-org-3337	109	56	2,2	2,2	CD
en-wikipedia-org-3337	109	57	)	)	-RRB-
en-wikipedia-org-3337	109	58	,	,	,
en-wikipedia-org-3337	109	59	and	and	CC
en-wikipedia-org-3337	109	60	(	(	-LRB-
en-wikipedia-org-3337	109	61	3,3	3,3	CD
en-wikipedia-org-3337	109	62	)	)	-RRB-
en-wikipedia-org-3337	109	63	.	.	.
en-wikipedia-org-3337	110	1	Nash	nash	JJ
en-wikipedia-org-3337	110	2	equilibria	equilibria	NN
en-wikipedia-org-3337	110	3	in	in	IN
en-wikipedia-org-3337	110	4	a	a	DT
en-wikipedia-org-3337	110	5	payoff	payoff	NN
en-wikipedia-org-3337	110	6	matrix[edit	matrix[edit	LS
en-wikipedia-org-3337	110	7	]	]	-RRB-
en-wikipedia-org-3337	110	8	There	there	EX
en-wikipedia-org-3337	110	9	is	be	VBZ
en-wikipedia-org-3337	110	10	an	an	DT
en-wikipedia-org-3337	110	11	easy	easy	JJ
en-wikipedia-org-3337	110	12	numerical	numerical	JJ
en-wikipedia-org-3337	110	13	way	way	NN
en-wikipedia-org-3337	110	14	to	to	TO
en-wikipedia-org-3337	110	15	identify	identify	VB
en-wikipedia-org-3337	110	16	Nash	Nash	NNP
en-wikipedia-org-3337	110	17	equilibria	equilibria	NN
en-wikipedia-org-3337	110	18	on	on	IN
en-wikipedia-org-3337	110	19	a	a	DT
en-wikipedia-org-3337	110	20	payoff	payoff	NN
en-wikipedia-org-3337	110	21	matrix	matrix	NN
en-wikipedia-org-3337	110	22	.	.	.
en-wikipedia-org-3337	111	1	It	-PRON-	PRP
en-wikipedia-org-3337	111	2	is	be	VBZ
en-wikipedia-org-3337	111	3	especially	especially	RB
en-wikipedia-org-3337	111	4	helpful	helpful	JJ
en-wikipedia-org-3337	111	5	in	in	IN
en-wikipedia-org-3337	111	6	two	two	CD
en-wikipedia-org-3337	111	7	-	-	HYPH
en-wikipedia-org-3337	111	8	person	person	NN
en-wikipedia-org-3337	111	9	games	game	NNS
en-wikipedia-org-3337	111	10	where	where	WRB
en-wikipedia-org-3337	111	11	players	player	NNS
en-wikipedia-org-3337	111	12	have	have	VBP
en-wikipedia-org-3337	111	13	more	more	JJR
en-wikipedia-org-3337	111	14	than	than	IN
en-wikipedia-org-3337	111	15	two	two	CD
en-wikipedia-org-3337	111	16	strategies	strategy	NNS
en-wikipedia-org-3337	111	17	.	.	.
en-wikipedia-org-3337	112	1	In	in	IN
en-wikipedia-org-3337	112	2	this	this	DT
en-wikipedia-org-3337	112	3	case	case	NN
en-wikipedia-org-3337	112	4	formal	formal	JJ
en-wikipedia-org-3337	112	5	analysis	analysis	NN
en-wikipedia-org-3337	112	6	may	may	MD
en-wikipedia-org-3337	112	7	become	become	VB
en-wikipedia-org-3337	112	8	too	too	RB
en-wikipedia-org-3337	112	9	long	long	RB
en-wikipedia-org-3337	112	10	.	.	.
en-wikipedia-org-3337	113	1	This	this	DT
en-wikipedia-org-3337	113	2	rule	rule	NN
en-wikipedia-org-3337	113	3	does	do	VBZ
en-wikipedia-org-3337	113	4	not	not	RB
en-wikipedia-org-3337	113	5	apply	apply	VB
en-wikipedia-org-3337	113	6	to	to	IN
en-wikipedia-org-3337	113	7	the	the	DT
en-wikipedia-org-3337	113	8	case	case	NN
en-wikipedia-org-3337	113	9	where	where	WRB
en-wikipedia-org-3337	113	10	mixed	mixed	JJ
en-wikipedia-org-3337	113	11	(	(	-LRB-
en-wikipedia-org-3337	113	12	stochastic	stochastic	JJ
en-wikipedia-org-3337	113	13	)	)	-RRB-
en-wikipedia-org-3337	113	14	strategies	strategy	NNS
en-wikipedia-org-3337	113	15	are	be	VBP
en-wikipedia-org-3337	113	16	of	of	IN
en-wikipedia-org-3337	113	17	interest	interest	NN
en-wikipedia-org-3337	113	18	.	.	.
en-wikipedia-org-3337	114	1	The	the	DT
en-wikipedia-org-3337	114	2	rule	rule	NN
en-wikipedia-org-3337	114	3	goes	go	VBZ
en-wikipedia-org-3337	114	4	as	as	IN
en-wikipedia-org-3337	114	5	follows	follow	VBZ
en-wikipedia-org-3337	114	6	:	:	:
en-wikipedia-org-3337	114	7	if	if	IN
en-wikipedia-org-3337	114	8	the	the	DT
en-wikipedia-org-3337	114	9	first	first	JJ
en-wikipedia-org-3337	114	10	payoff	payoff	NN
en-wikipedia-org-3337	114	11	number	number	NN
en-wikipedia-org-3337	114	12	,	,	,
en-wikipedia-org-3337	114	13	in	in	IN
en-wikipedia-org-3337	114	14	the	the	DT
en-wikipedia-org-3337	114	15	payoff	payoff	NN
en-wikipedia-org-3337	114	16	pair	pair	NN
en-wikipedia-org-3337	114	17	of	of	IN
en-wikipedia-org-3337	114	18	the	the	DT
en-wikipedia-org-3337	114	19	cell	cell	NN
en-wikipedia-org-3337	114	20	,	,	,
en-wikipedia-org-3337	114	21	is	be	VBZ
en-wikipedia-org-3337	114	22	the	the	DT
en-wikipedia-org-3337	114	23	maximum	maximum	NN
en-wikipedia-org-3337	114	24	of	of	IN
en-wikipedia-org-3337	114	25	the	the	DT
en-wikipedia-org-3337	114	26	column	column	NN
en-wikipedia-org-3337	114	27	of	of	IN
en-wikipedia-org-3337	114	28	the	the	DT
en-wikipedia-org-3337	114	29	cell	cell	NN
en-wikipedia-org-3337	114	30	and	and	CC
en-wikipedia-org-3337	114	31	if	if	IN
en-wikipedia-org-3337	114	32	the	the	DT
en-wikipedia-org-3337	114	33	second	second	JJ
en-wikipedia-org-3337	114	34	number	number	NN
en-wikipedia-org-3337	114	35	is	be	VBZ
en-wikipedia-org-3337	114	36	the	the	DT
en-wikipedia-org-3337	114	37	maximum	maximum	NN
en-wikipedia-org-3337	114	38	of	of	IN
en-wikipedia-org-3337	114	39	the	the	DT
en-wikipedia-org-3337	114	40	row	row	NN
en-wikipedia-org-3337	114	41	of	of	IN
en-wikipedia-org-3337	114	42	the	the	DT
en-wikipedia-org-3337	114	43	cell	cell	NN
en-wikipedia-org-3337	114	44	-	-	:
en-wikipedia-org-3337	114	45	then	then	RB
en-wikipedia-org-3337	114	46	the	the	DT
en-wikipedia-org-3337	114	47	cell	cell	NN
en-wikipedia-org-3337	114	48	represents	represent	VBZ
en-wikipedia-org-3337	114	49	a	a	DT
en-wikipedia-org-3337	114	50	Nash	Nash	NNP
en-wikipedia-org-3337	114	51	equilibrium	equilibrium	NN
en-wikipedia-org-3337	114	52	.	.	.
en-wikipedia-org-3337	115	1	A	a	DT
en-wikipedia-org-3337	115	2	payoff	payoff	NN
en-wikipedia-org-3337	115	3	matrix	matrix	NN
en-wikipedia-org-3337	115	4	–	–	:
en-wikipedia-org-3337	115	5	Nash	Nash	NNP
en-wikipedia-org-3337	115	6	equilibria	equilibria	NN
en-wikipedia-org-3337	115	7	in	in	IN
en-wikipedia-org-3337	115	8	bold	bold	JJ
en-wikipedia-org-3337	115	9	Player	Player	NNP
en-wikipedia-org-3337	115	10	2	2	CD
en-wikipedia-org-3337	115	11	Player	player	NN
en-wikipedia-org-3337	115	12	1	1	CD
en-wikipedia-org-3337	115	13	Option	option	NN
en-wikipedia-org-3337	115	14	A	A	NNP
en-wikipedia-org-3337	115	15	Option	Option	NNP
en-wikipedia-org-3337	115	16	B	B	NNP
en-wikipedia-org-3337	115	17	Option	option	NN
en-wikipedia-org-3337	115	18	C	c	NN
en-wikipedia-org-3337	115	19	Option	Option	NNP
en-wikipedia-org-3337	115	20	A	A	NNP
en-wikipedia-org-3337	115	21	0	0	CD
en-wikipedia-org-3337	115	22	,	,	,
en-wikipedia-org-3337	115	23	0	0	CD
en-wikipedia-org-3337	115	24	25	25	CD
en-wikipedia-org-3337	115	25	,	,	,
en-wikipedia-org-3337	115	26	40	40	CD
en-wikipedia-org-3337	115	27	5	5	CD
en-wikipedia-org-3337	115	28	,	,	,
en-wikipedia-org-3337	115	29	10	10	CD
en-wikipedia-org-3337	115	30	Option	option	NN
en-wikipedia-org-3337	115	31	B	B	NNP
en-wikipedia-org-3337	115	32	40	40	CD
en-wikipedia-org-3337	115	33	,	,	,
en-wikipedia-org-3337	115	34	25	25	CD
en-wikipedia-org-3337	115	35	0	0	CD
en-wikipedia-org-3337	115	36	,	,	,
en-wikipedia-org-3337	115	37	0	0	CD
en-wikipedia-org-3337	115	38	5	5	CD
en-wikipedia-org-3337	115	39	,	,	,
en-wikipedia-org-3337	115	40	15	15	CD
en-wikipedia-org-3337	115	41	Option	option	NN
en-wikipedia-org-3337	115	42	C	C	NNP
en-wikipedia-org-3337	115	43	10	10	CD
en-wikipedia-org-3337	115	44	,	,	,
en-wikipedia-org-3337	115	45	5	5	CD
en-wikipedia-org-3337	115	46	15	15	CD
en-wikipedia-org-3337	115	47	,	,	,
en-wikipedia-org-3337	115	48	5	5	CD
en-wikipedia-org-3337	115	49	10	10	CD
en-wikipedia-org-3337	115	50	,	,	,
en-wikipedia-org-3337	115	51	10	10	CD
en-wikipedia-org-3337	115	52	We	-PRON-	PRP
en-wikipedia-org-3337	115	53	can	can	MD
en-wikipedia-org-3337	115	54	apply	apply	VB
en-wikipedia-org-3337	115	55	this	this	DT
en-wikipedia-org-3337	115	56	rule	rule	NN
en-wikipedia-org-3337	115	57	to	to	IN
en-wikipedia-org-3337	115	58	a	a	DT
en-wikipedia-org-3337	115	59	3×3	3×3	CD
en-wikipedia-org-3337	115	60	matrix	matrix	NN
en-wikipedia-org-3337	115	61	:	:	:
en-wikipedia-org-3337	115	62	Using	use	VBG
en-wikipedia-org-3337	115	63	the	the	DT
en-wikipedia-org-3337	115	64	rule	rule	NN
en-wikipedia-org-3337	115	65	,	,	,
en-wikipedia-org-3337	115	66	we	-PRON-	PRP
en-wikipedia-org-3337	115	67	can	can	MD
en-wikipedia-org-3337	115	68	very	very	RB
en-wikipedia-org-3337	115	69	quickly	quickly	RB
en-wikipedia-org-3337	115	70	(	(	-LRB-
en-wikipedia-org-3337	115	71	much	much	RB
en-wikipedia-org-3337	115	72	faster	fast	RBR
en-wikipedia-org-3337	115	73	than	than	IN
en-wikipedia-org-3337	115	74	with	with	IN
en-wikipedia-org-3337	115	75	formal	formal	JJ
en-wikipedia-org-3337	115	76	analysis	analysis	NN
en-wikipedia-org-3337	115	77	)	)	-RRB-
en-wikipedia-org-3337	115	78	see	see	VBP
en-wikipedia-org-3337	115	79	that	that	IN
en-wikipedia-org-3337	115	80	the	the	DT
en-wikipedia-org-3337	115	81	Nash	Nash	NNP
en-wikipedia-org-3337	115	82	equilibria	equilibria	NN
en-wikipedia-org-3337	115	83	cells	cell	NNS
en-wikipedia-org-3337	115	84	are	be	VBP
en-wikipedia-org-3337	115	85	(	(	-LRB-
en-wikipedia-org-3337	115	86	B	b	UH
en-wikipedia-org-3337	115	87	,	,	,
en-wikipedia-org-3337	115	88	A	a	NN
en-wikipedia-org-3337	115	89	)	)	-RRB-
en-wikipedia-org-3337	115	90	,	,	,
en-wikipedia-org-3337	115	91	(	(	-LRB-
en-wikipedia-org-3337	115	92	A	a	NN
en-wikipedia-org-3337	115	93	,	,	,
en-wikipedia-org-3337	115	94	B	b	NN
en-wikipedia-org-3337	115	95	)	)	-RRB-
en-wikipedia-org-3337	115	96	,	,	,
en-wikipedia-org-3337	115	97	and	and	CC
en-wikipedia-org-3337	115	98	(	(	-LRB-
en-wikipedia-org-3337	115	99	C	C	NNP
en-wikipedia-org-3337	115	100	,	,	,
en-wikipedia-org-3337	115	101	C	C	NNP
en-wikipedia-org-3337	115	102	)	)	-RRB-
en-wikipedia-org-3337	115	103	.	.	.
en-wikipedia-org-3337	116	1	Indeed	indeed	RB
en-wikipedia-org-3337	116	2	,	,	,
en-wikipedia-org-3337	116	3	for	for	IN
en-wikipedia-org-3337	116	4	cell	cell	NN
en-wikipedia-org-3337	116	5	(	(	-LRB-
en-wikipedia-org-3337	116	6	B	b	NN
en-wikipedia-org-3337	116	7	,	,	,
en-wikipedia-org-3337	116	8	A	a	NN
en-wikipedia-org-3337	116	9	)	)	-RRB-
en-wikipedia-org-3337	116	10	40	40	CD
en-wikipedia-org-3337	116	11	is	be	VBZ
en-wikipedia-org-3337	116	12	the	the	DT
en-wikipedia-org-3337	116	13	maximum	maximum	NN
en-wikipedia-org-3337	116	14	of	of	IN
en-wikipedia-org-3337	116	15	the	the	DT
en-wikipedia-org-3337	116	16	first	first	JJ
en-wikipedia-org-3337	116	17	column	column	NN
en-wikipedia-org-3337	116	18	and	and	CC
en-wikipedia-org-3337	116	19	25	25	CD
en-wikipedia-org-3337	116	20	is	be	VBZ
en-wikipedia-org-3337	116	21	the	the	DT
en-wikipedia-org-3337	116	22	maximum	maximum	NN
en-wikipedia-org-3337	116	23	of	of	IN
en-wikipedia-org-3337	116	24	the	the	DT
en-wikipedia-org-3337	116	25	second	second	JJ
en-wikipedia-org-3337	116	26	row	row	NN
en-wikipedia-org-3337	116	27	.	.	.
en-wikipedia-org-3337	117	1	For	for	IN
en-wikipedia-org-3337	117	2	(	(	-LRB-
en-wikipedia-org-3337	117	3	A	a	NN
en-wikipedia-org-3337	117	4	,	,	,
en-wikipedia-org-3337	117	5	B	b	NN
en-wikipedia-org-3337	117	6	)	)	-RRB-
en-wikipedia-org-3337	117	7	25	25	CD
en-wikipedia-org-3337	117	8	is	be	VBZ
en-wikipedia-org-3337	117	9	the	the	DT
en-wikipedia-org-3337	117	10	maximum	maximum	NN
en-wikipedia-org-3337	117	11	of	of	IN
en-wikipedia-org-3337	117	12	the	the	DT
en-wikipedia-org-3337	117	13	second	second	JJ
en-wikipedia-org-3337	117	14	column	column	NN
en-wikipedia-org-3337	117	15	and	and	CC
en-wikipedia-org-3337	117	16	40	40	CD
en-wikipedia-org-3337	117	17	is	be	VBZ
en-wikipedia-org-3337	117	18	the	the	DT
en-wikipedia-org-3337	117	19	maximum	maximum	NN
en-wikipedia-org-3337	117	20	of	of	IN
en-wikipedia-org-3337	117	21	the	the	DT
en-wikipedia-org-3337	117	22	first	first	JJ
en-wikipedia-org-3337	117	23	row	row	NN
en-wikipedia-org-3337	117	24	.	.	.
en-wikipedia-org-3337	118	1	Same	same	JJ
en-wikipedia-org-3337	118	2	for	for	IN
en-wikipedia-org-3337	118	3	cell	cell	NN
en-wikipedia-org-3337	118	4	(	(	-LRB-
en-wikipedia-org-3337	118	5	C	C	NNP
en-wikipedia-org-3337	118	6	,	,	,
en-wikipedia-org-3337	118	7	C	C	NNP
en-wikipedia-org-3337	118	8	)	)	-RRB-
en-wikipedia-org-3337	118	9	.	.	.
en-wikipedia-org-3337	119	1	For	for	IN
en-wikipedia-org-3337	119	2	other	other	JJ
en-wikipedia-org-3337	119	3	cells	cell	NNS
en-wikipedia-org-3337	119	4	,	,	,
en-wikipedia-org-3337	119	5	either	either	CC
en-wikipedia-org-3337	119	6	one	one	CD
en-wikipedia-org-3337	119	7	or	or	CC
en-wikipedia-org-3337	119	8	both	both	DT
en-wikipedia-org-3337	119	9	of	of	IN
en-wikipedia-org-3337	119	10	the	the	DT
en-wikipedia-org-3337	119	11	duplet	duplet	NNP
en-wikipedia-org-3337	119	12	members	member	NNS
en-wikipedia-org-3337	119	13	are	be	VBP
en-wikipedia-org-3337	119	14	not	not	RB
en-wikipedia-org-3337	119	15	the	the	DT
en-wikipedia-org-3337	119	16	maximum	maximum	NN
en-wikipedia-org-3337	119	17	of	of	IN
en-wikipedia-org-3337	119	18	the	the	DT
en-wikipedia-org-3337	119	19	corresponding	correspond	VBG
en-wikipedia-org-3337	119	20	rows	row	NNS
en-wikipedia-org-3337	119	21	and	and	CC
en-wikipedia-org-3337	119	22	columns	column	NNS
en-wikipedia-org-3337	119	23	.	.	.
en-wikipedia-org-3337	120	1	This	this	DT
en-wikipedia-org-3337	120	2	said	say	VBD
en-wikipedia-org-3337	120	3	,	,	,
en-wikipedia-org-3337	120	4	the	the	DT
en-wikipedia-org-3337	120	5	actual	actual	JJ
en-wikipedia-org-3337	120	6	mechanics	mechanic	NNS
en-wikipedia-org-3337	120	7	of	of	IN
en-wikipedia-org-3337	120	8	finding	find	VBG
en-wikipedia-org-3337	120	9	equilibrium	equilibrium	NN
en-wikipedia-org-3337	120	10	cells	cell	NNS
en-wikipedia-org-3337	120	11	is	be	VBZ
en-wikipedia-org-3337	120	12	obvious	obvious	JJ
en-wikipedia-org-3337	120	13	:	:	:
en-wikipedia-org-3337	120	14	find	find	VB
en-wikipedia-org-3337	120	15	the	the	DT
en-wikipedia-org-3337	120	16	maximum	maximum	NN
en-wikipedia-org-3337	120	17	of	of	IN
en-wikipedia-org-3337	120	18	a	a	DT
en-wikipedia-org-3337	120	19	column	column	NN
en-wikipedia-org-3337	120	20	and	and	CC
en-wikipedia-org-3337	120	21	check	check	VB
en-wikipedia-org-3337	120	22	if	if	IN
en-wikipedia-org-3337	120	23	the	the	DT
en-wikipedia-org-3337	120	24	second	second	JJ
en-wikipedia-org-3337	120	25	member	member	NN
en-wikipedia-org-3337	120	26	of	of	IN
en-wikipedia-org-3337	120	27	the	the	DT
en-wikipedia-org-3337	120	28	pair	pair	NN
en-wikipedia-org-3337	120	29	is	be	VBZ
en-wikipedia-org-3337	120	30	the	the	DT
en-wikipedia-org-3337	120	31	maximum	maximum	NN
en-wikipedia-org-3337	120	32	of	of	IN
en-wikipedia-org-3337	120	33	the	the	DT
en-wikipedia-org-3337	120	34	row	row	NN
en-wikipedia-org-3337	120	35	.	.	.
en-wikipedia-org-3337	121	1	If	if	IN
en-wikipedia-org-3337	121	2	these	these	DT
en-wikipedia-org-3337	121	3	conditions	condition	NNS
en-wikipedia-org-3337	121	4	are	be	VBP
en-wikipedia-org-3337	121	5	met	meet	VBN
en-wikipedia-org-3337	121	6	,	,	,
en-wikipedia-org-3337	121	7	the	the	DT
en-wikipedia-org-3337	121	8	cell	cell	NN
en-wikipedia-org-3337	121	9	represents	represent	VBZ
en-wikipedia-org-3337	121	10	a	a	DT
en-wikipedia-org-3337	121	11	Nash	Nash	NNP
en-wikipedia-org-3337	121	12	equilibrium	equilibrium	NN
en-wikipedia-org-3337	121	13	.	.	.
en-wikipedia-org-3337	122	1	Check	check	VB
en-wikipedia-org-3337	122	2	all	all	DT
en-wikipedia-org-3337	122	3	columns	column	NNS
en-wikipedia-org-3337	122	4	this	this	DT
en-wikipedia-org-3337	122	5	way	way	NN
en-wikipedia-org-3337	122	6	to	to	TO
en-wikipedia-org-3337	122	7	find	find	VB
en-wikipedia-org-3337	122	8	all	all	DT
en-wikipedia-org-3337	122	9	NE	NE	NNP
en-wikipedia-org-3337	122	10	cells	cell	NNS
en-wikipedia-org-3337	122	11	.	.	.
en-wikipedia-org-3337	123	1	An	an	DT
en-wikipedia-org-3337	123	2	N×N	N×N	NNS
en-wikipedia-org-3337	123	3	matrix	matrix	NN
en-wikipedia-org-3337	123	4	may	may	MD
en-wikipedia-org-3337	123	5	have	have	VB
en-wikipedia-org-3337	123	6	between	between	IN
en-wikipedia-org-3337	123	7	0	0	CD
en-wikipedia-org-3337	123	8	and	and	CC
en-wikipedia-org-3337	123	9	N×N	n×n	CD
en-wikipedia-org-3337	123	10	pure	pure	JJ
en-wikipedia-org-3337	123	11	-	-	HYPH
en-wikipedia-org-3337	123	12	strategy	strategy	NN
en-wikipedia-org-3337	123	13	Nash	Nash	NNP
en-wikipedia-org-3337	123	14	equilibria	equilibria	NN
en-wikipedia-org-3337	123	15	.	.	.
en-wikipedia-org-3337	124	1	Stability[edit	stability[edit	LS
en-wikipedia-org-3337	124	2	]	]	-RRB-
en-wikipedia-org-3337	124	3	The	the	DT
en-wikipedia-org-3337	124	4	concept	concept	NN
en-wikipedia-org-3337	124	5	of	of	IN
en-wikipedia-org-3337	124	6	stability	stability	NN
en-wikipedia-org-3337	124	7	,	,	,
en-wikipedia-org-3337	124	8	useful	useful	JJ
en-wikipedia-org-3337	124	9	in	in	IN
en-wikipedia-org-3337	124	10	the	the	DT
en-wikipedia-org-3337	124	11	analysis	analysis	NN
en-wikipedia-org-3337	124	12	of	of	IN
en-wikipedia-org-3337	124	13	many	many	JJ
en-wikipedia-org-3337	124	14	kinds	kind	NNS
en-wikipedia-org-3337	124	15	of	of	IN
en-wikipedia-org-3337	124	16	equilibria	equilibria	NN
en-wikipedia-org-3337	124	17	,	,	,
en-wikipedia-org-3337	124	18	can	can	MD
en-wikipedia-org-3337	124	19	also	also	RB
en-wikipedia-org-3337	124	20	be	be	VB
en-wikipedia-org-3337	124	21	applied	apply	VBN
en-wikipedia-org-3337	124	22	to	to	IN
en-wikipedia-org-3337	124	23	Nash	Nash	NNP
en-wikipedia-org-3337	124	24	equilibria	equilibria	NN
en-wikipedia-org-3337	124	25	.	.	.
en-wikipedia-org-3337	125	1	A	a	DT
en-wikipedia-org-3337	125	2	Nash	Nash	NNP
en-wikipedia-org-3337	125	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	125	4	for	for	IN
en-wikipedia-org-3337	125	5	a	a	DT
en-wikipedia-org-3337	125	6	mixed	mixed	JJ
en-wikipedia-org-3337	125	7	-	-	HYPH
en-wikipedia-org-3337	125	8	strategy	strategy	NN
en-wikipedia-org-3337	125	9	game	game	NN
en-wikipedia-org-3337	125	10	is	be	VBZ
en-wikipedia-org-3337	125	11	stable	stable	JJ
en-wikipedia-org-3337	125	12	if	if	IN
en-wikipedia-org-3337	125	13	a	a	DT
en-wikipedia-org-3337	125	14	small	small	JJ
en-wikipedia-org-3337	125	15	change	change	NN
en-wikipedia-org-3337	125	16	(	(	-LRB-
en-wikipedia-org-3337	125	17	specifically	specifically	RB
en-wikipedia-org-3337	125	18	,	,	,
en-wikipedia-org-3337	125	19	an	an	DT
en-wikipedia-org-3337	125	20	infinitesimal	infinitesimal	JJ
en-wikipedia-org-3337	125	21	change	change	NN
en-wikipedia-org-3337	125	22	)	)	-RRB-
en-wikipedia-org-3337	125	23	in	in	IN
en-wikipedia-org-3337	125	24	probabilities	probability	NNS
en-wikipedia-org-3337	125	25	for	for	IN
en-wikipedia-org-3337	125	26	one	one	CD
en-wikipedia-org-3337	125	27	player	player	NN
en-wikipedia-org-3337	125	28	leads	lead	VBZ
en-wikipedia-org-3337	125	29	to	to	IN
en-wikipedia-org-3337	125	30	a	a	DT
en-wikipedia-org-3337	125	31	situation	situation	NN
en-wikipedia-org-3337	125	32	where	where	WRB
en-wikipedia-org-3337	125	33	two	two	CD
en-wikipedia-org-3337	125	34	conditions	condition	NNS
en-wikipedia-org-3337	125	35	hold	hold	VBP
en-wikipedia-org-3337	125	36	:	:	:
en-wikipedia-org-3337	125	37	the	the	DT
en-wikipedia-org-3337	125	38	player	player	NN
en-wikipedia-org-3337	125	39	who	who	WP
en-wikipedia-org-3337	125	40	did	do	VBD
en-wikipedia-org-3337	125	41	not	not	RB
en-wikipedia-org-3337	125	42	change	change	VB
en-wikipedia-org-3337	125	43	has	have	VBZ
en-wikipedia-org-3337	125	44	no	no	DT
en-wikipedia-org-3337	125	45	better	well	JJR
en-wikipedia-org-3337	125	46	strategy	strategy	NN
en-wikipedia-org-3337	125	47	in	in	IN
en-wikipedia-org-3337	125	48	the	the	DT
en-wikipedia-org-3337	125	49	new	new	JJ
en-wikipedia-org-3337	125	50	circumstance	circumstance	NN
en-wikipedia-org-3337	125	51	the	the	DT
en-wikipedia-org-3337	125	52	player	player	NN
en-wikipedia-org-3337	125	53	who	who	WP
en-wikipedia-org-3337	125	54	did	do	VBD
en-wikipedia-org-3337	125	55	change	change	NN
en-wikipedia-org-3337	125	56	is	be	VBZ
en-wikipedia-org-3337	125	57	now	now	RB
en-wikipedia-org-3337	125	58	playing	play	VBG
en-wikipedia-org-3337	125	59	with	with	IN
en-wikipedia-org-3337	125	60	a	a	DT
en-wikipedia-org-3337	125	61	strictly	strictly	RB
en-wikipedia-org-3337	125	62	worse	bad	JJR
en-wikipedia-org-3337	125	63	strategy	strategy	NN
en-wikipedia-org-3337	125	64	.	.	.
en-wikipedia-org-3337	126	1	If	if	IN
en-wikipedia-org-3337	126	2	these	these	DT
en-wikipedia-org-3337	126	3	cases	case	NNS
en-wikipedia-org-3337	126	4	are	be	VBP
en-wikipedia-org-3337	126	5	both	both	DT
en-wikipedia-org-3337	126	6	met	meet	VBN
en-wikipedia-org-3337	126	7	,	,	,
en-wikipedia-org-3337	126	8	then	then	RB
en-wikipedia-org-3337	126	9	a	a	DT
en-wikipedia-org-3337	126	10	player	player	NN
en-wikipedia-org-3337	126	11	with	with	IN
en-wikipedia-org-3337	126	12	the	the	DT
en-wikipedia-org-3337	126	13	small	small	JJ
en-wikipedia-org-3337	126	14	change	change	NN
en-wikipedia-org-3337	126	15	in	in	IN
en-wikipedia-org-3337	126	16	their	-PRON-	PRP$
en-wikipedia-org-3337	126	17	mixed	mix	VBN
en-wikipedia-org-3337	126	18	strategy	strategy	NN
en-wikipedia-org-3337	126	19	will	will	MD
en-wikipedia-org-3337	126	20	return	return	VB
en-wikipedia-org-3337	126	21	immediately	immediately	RB
en-wikipedia-org-3337	126	22	to	to	IN
en-wikipedia-org-3337	126	23	the	the	DT
en-wikipedia-org-3337	126	24	Nash	Nash	NNP
en-wikipedia-org-3337	126	25	equilibrium	equilibrium	NN
en-wikipedia-org-3337	126	26	.	.	.
en-wikipedia-org-3337	127	1	The	the	DT
en-wikipedia-org-3337	127	2	equilibrium	equilibrium	NN
en-wikipedia-org-3337	127	3	is	be	VBZ
en-wikipedia-org-3337	127	4	said	say	VBN
en-wikipedia-org-3337	127	5	to	to	TO
en-wikipedia-org-3337	127	6	be	be	VB
en-wikipedia-org-3337	127	7	stable	stable	JJ
en-wikipedia-org-3337	127	8	.	.	.
en-wikipedia-org-3337	128	1	If	if	IN
en-wikipedia-org-3337	128	2	condition	condition	NN
en-wikipedia-org-3337	128	3	one	one	NN
en-wikipedia-org-3337	128	4	does	do	VBZ
en-wikipedia-org-3337	128	5	not	not	RB
en-wikipedia-org-3337	128	6	hold	hold	VB
en-wikipedia-org-3337	128	7	then	then	RB
en-wikipedia-org-3337	128	8	the	the	DT
en-wikipedia-org-3337	128	9	equilibrium	equilibrium	NN
en-wikipedia-org-3337	128	10	is	be	VBZ
en-wikipedia-org-3337	128	11	unstable	unstable	JJ
en-wikipedia-org-3337	128	12	.	.	.
en-wikipedia-org-3337	129	1	If	if	IN
en-wikipedia-org-3337	129	2	only	only	RB
en-wikipedia-org-3337	129	3	condition	condition	NN
en-wikipedia-org-3337	129	4	one	one	NN
en-wikipedia-org-3337	129	5	holds	hold	VBZ
en-wikipedia-org-3337	129	6	then	then	RB
en-wikipedia-org-3337	129	7	there	there	EX
en-wikipedia-org-3337	129	8	are	be	VBP
en-wikipedia-org-3337	129	9	likely	likely	JJ
en-wikipedia-org-3337	129	10	to	to	TO
en-wikipedia-org-3337	129	11	be	be	VB
en-wikipedia-org-3337	129	12	an	an	DT
en-wikipedia-org-3337	129	13	infinite	infinite	JJ
en-wikipedia-org-3337	129	14	number	number	NN
en-wikipedia-org-3337	129	15	of	of	IN
en-wikipedia-org-3337	129	16	optimal	optimal	JJ
en-wikipedia-org-3337	129	17	strategies	strategy	NNS
en-wikipedia-org-3337	129	18	for	for	IN
en-wikipedia-org-3337	129	19	the	the	DT
en-wikipedia-org-3337	129	20	player	player	NN
en-wikipedia-org-3337	129	21	who	who	WP
en-wikipedia-org-3337	129	22	changed	change	VBD
en-wikipedia-org-3337	129	23	.	.	.
en-wikipedia-org-3337	130	1	In	in	IN
en-wikipedia-org-3337	130	2	the	the	DT
en-wikipedia-org-3337	130	3	"	"	``
en-wikipedia-org-3337	130	4	driving	driving	NN
en-wikipedia-org-3337	130	5	game	game	NN
en-wikipedia-org-3337	130	6	"	"	''
en-wikipedia-org-3337	130	7	example	example	NN
en-wikipedia-org-3337	130	8	above	above	IN
en-wikipedia-org-3337	130	9	there	there	EX
en-wikipedia-org-3337	130	10	are	be	VBP
en-wikipedia-org-3337	130	11	both	both	DT
en-wikipedia-org-3337	130	12	stable	stable	JJ
en-wikipedia-org-3337	130	13	and	and	CC
en-wikipedia-org-3337	130	14	unstable	unstable	JJ
en-wikipedia-org-3337	130	15	equilibria	equilibria	NN
en-wikipedia-org-3337	130	16	.	.	.
en-wikipedia-org-3337	131	1	The	the	DT
en-wikipedia-org-3337	131	2	equilibria	equilibria	NN
en-wikipedia-org-3337	131	3	involving	involve	VBG
en-wikipedia-org-3337	131	4	mixed	mix	VBN
en-wikipedia-org-3337	131	5	strategies	strategy	NNS
en-wikipedia-org-3337	131	6	with	with	IN
en-wikipedia-org-3337	131	7	100	100	CD
en-wikipedia-org-3337	131	8	%	%	NN
en-wikipedia-org-3337	131	9	probabilities	probability	NNS
en-wikipedia-org-3337	131	10	are	be	VBP
en-wikipedia-org-3337	131	11	stable	stable	JJ
en-wikipedia-org-3337	131	12	.	.	.
en-wikipedia-org-3337	132	1	If	if	IN
en-wikipedia-org-3337	132	2	either	either	DT
en-wikipedia-org-3337	132	3	player	player	NN
en-wikipedia-org-3337	132	4	changes	change	VBZ
en-wikipedia-org-3337	132	5	their	-PRON-	PRP$
en-wikipedia-org-3337	132	6	probabilities	probability	NNS
en-wikipedia-org-3337	132	7	slightly	slightly	RB
en-wikipedia-org-3337	132	8	,	,	,
en-wikipedia-org-3337	132	9	they	-PRON-	PRP
en-wikipedia-org-3337	132	10	will	will	MD
en-wikipedia-org-3337	132	11	be	be	VB
en-wikipedia-org-3337	132	12	both	both	DT
en-wikipedia-org-3337	132	13	at	at	IN
en-wikipedia-org-3337	132	14	a	a	DT
en-wikipedia-org-3337	132	15	disadvantage	disadvantage	NN
en-wikipedia-org-3337	132	16	,	,	,
en-wikipedia-org-3337	132	17	and	and	CC
en-wikipedia-org-3337	132	18	their	-PRON-	PRP$
en-wikipedia-org-3337	132	19	opponent	opponent	NN
en-wikipedia-org-3337	132	20	will	will	MD
en-wikipedia-org-3337	132	21	have	have	VB
en-wikipedia-org-3337	132	22	no	no	DT
en-wikipedia-org-3337	132	23	reason	reason	NN
en-wikipedia-org-3337	132	24	to	to	TO
en-wikipedia-org-3337	132	25	change	change	VB
en-wikipedia-org-3337	132	26	their	-PRON-	PRP$
en-wikipedia-org-3337	132	27	strategy	strategy	NN
en-wikipedia-org-3337	132	28	in	in	IN
en-wikipedia-org-3337	132	29	turn	turn	NN
en-wikipedia-org-3337	132	30	.	.	.
en-wikipedia-org-3337	133	1	The	the	DT
en-wikipedia-org-3337	133	2	(	(	-LRB-
en-wikipedia-org-3337	133	3	50%,50	50%,50	CD
en-wikipedia-org-3337	133	4	%	%	NN
en-wikipedia-org-3337	133	5	)	)	-RRB-
en-wikipedia-org-3337	133	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	133	7	is	be	VBZ
en-wikipedia-org-3337	133	8	unstable	unstable	JJ
en-wikipedia-org-3337	133	9	.	.	.
en-wikipedia-org-3337	134	1	If	if	IN
en-wikipedia-org-3337	134	2	either	either	DT
en-wikipedia-org-3337	134	3	player	player	NN
en-wikipedia-org-3337	134	4	changes	change	VBZ
en-wikipedia-org-3337	134	5	their	-PRON-	PRP$
en-wikipedia-org-3337	134	6	probabilities	probability	NNS
en-wikipedia-org-3337	134	7	(	(	-LRB-
en-wikipedia-org-3337	134	8	which	which	WDT
en-wikipedia-org-3337	134	9	would	would	MD
en-wikipedia-org-3337	134	10	neither	neither	CC
en-wikipedia-org-3337	134	11	benefit	benefit	VB
en-wikipedia-org-3337	134	12	or	or	CC
en-wikipedia-org-3337	134	13	damage	damage	VB
en-wikipedia-org-3337	134	14	the	the	DT
en-wikipedia-org-3337	134	15	expectation	expectation	NN
en-wikipedia-org-3337	134	16	of	of	IN
en-wikipedia-org-3337	134	17	the	the	DT
en-wikipedia-org-3337	134	18	player	player	NN
en-wikipedia-org-3337	134	19	who	who	WP
en-wikipedia-org-3337	134	20	did	do	VBD
en-wikipedia-org-3337	134	21	the	the	DT
en-wikipedia-org-3337	134	22	change	change	NN
en-wikipedia-org-3337	134	23	,	,	,
en-wikipedia-org-3337	134	24	if	if	IN
en-wikipedia-org-3337	134	25	the	the	DT
en-wikipedia-org-3337	134	26	other	other	JJ
en-wikipedia-org-3337	134	27	player	player	NN
en-wikipedia-org-3337	134	28	's	's	POS
en-wikipedia-org-3337	134	29	mixed	mixed	JJ
en-wikipedia-org-3337	134	30	strategy	strategy	NN
en-wikipedia-org-3337	134	31	is	be	VBZ
en-wikipedia-org-3337	134	32	still	still	RB
en-wikipedia-org-3337	134	33	(	(	-LRB-
en-wikipedia-org-3337	134	34	50%,50	50%,50	CD
en-wikipedia-org-3337	134	35	%	%	NN
en-wikipedia-org-3337	134	36	)	)	-RRB-
en-wikipedia-org-3337	134	37	)	)	-RRB-
en-wikipedia-org-3337	134	38	,	,	,
en-wikipedia-org-3337	134	39	then	then	RB
en-wikipedia-org-3337	134	40	the	the	DT
en-wikipedia-org-3337	134	41	other	other	JJ
en-wikipedia-org-3337	134	42	player	player	NN
en-wikipedia-org-3337	134	43	immediately	immediately	RB
en-wikipedia-org-3337	134	44	has	have	VBZ
en-wikipedia-org-3337	134	45	a	a	DT
en-wikipedia-org-3337	134	46	better	well	JJR
en-wikipedia-org-3337	134	47	strategy	strategy	NN
en-wikipedia-org-3337	134	48	at	at	IN
en-wikipedia-org-3337	134	49	either	either	DT
en-wikipedia-org-3337	134	50	(	(	-LRB-
en-wikipedia-org-3337	134	51	0	0	CD
en-wikipedia-org-3337	134	52	%	%	NN
en-wikipedia-org-3337	134	53	,	,	,
en-wikipedia-org-3337	134	54	100	100	CD
en-wikipedia-org-3337	134	55	%	%	NN
en-wikipedia-org-3337	134	56	)	)	-RRB-
en-wikipedia-org-3337	134	57	or	or	CC
en-wikipedia-org-3337	134	58	(	(	-LRB-
en-wikipedia-org-3337	134	59	100	100	CD
en-wikipedia-org-3337	134	60	%	%	NN
en-wikipedia-org-3337	134	61	,	,	,
en-wikipedia-org-3337	134	62	0	0	CD
en-wikipedia-org-3337	134	63	%	%	NN
en-wikipedia-org-3337	134	64	)	)	-RRB-
en-wikipedia-org-3337	134	65	.	.	.
en-wikipedia-org-3337	135	1	Stability	stability	NN
en-wikipedia-org-3337	135	2	is	be	VBZ
en-wikipedia-org-3337	135	3	crucial	crucial	JJ
en-wikipedia-org-3337	135	4	in	in	IN
en-wikipedia-org-3337	135	5	practical	practical	JJ
en-wikipedia-org-3337	135	6	applications	application	NNS
en-wikipedia-org-3337	135	7	of	of	IN
en-wikipedia-org-3337	135	8	Nash	Nash	NNP
en-wikipedia-org-3337	135	9	equilibria	equilibria	NN
en-wikipedia-org-3337	135	10	,	,	,
en-wikipedia-org-3337	135	11	since	since	IN
en-wikipedia-org-3337	135	12	the	the	DT
en-wikipedia-org-3337	135	13	mixed	mixed	JJ
en-wikipedia-org-3337	135	14	strategy	strategy	NN
en-wikipedia-org-3337	135	15	of	of	IN
en-wikipedia-org-3337	135	16	each	each	DT
en-wikipedia-org-3337	135	17	player	player	NN
en-wikipedia-org-3337	135	18	is	be	VBZ
en-wikipedia-org-3337	135	19	not	not	RB
en-wikipedia-org-3337	135	20	perfectly	perfectly	RB
en-wikipedia-org-3337	135	21	known	know	VBN
en-wikipedia-org-3337	135	22	,	,	,
en-wikipedia-org-3337	135	23	but	but	CC
en-wikipedia-org-3337	135	24	has	have	VBZ
en-wikipedia-org-3337	135	25	to	to	TO
en-wikipedia-org-3337	135	26	be	be	VB
en-wikipedia-org-3337	135	27	inferred	infer	VBN
en-wikipedia-org-3337	135	28	from	from	IN
en-wikipedia-org-3337	135	29	statistical	statistical	JJ
en-wikipedia-org-3337	135	30	distribution	distribution	NN
en-wikipedia-org-3337	135	31	of	of	IN
en-wikipedia-org-3337	135	32	their	-PRON-	PRP$
en-wikipedia-org-3337	135	33	actions	action	NNS
en-wikipedia-org-3337	135	34	in	in	IN
en-wikipedia-org-3337	135	35	the	the	DT
en-wikipedia-org-3337	135	36	game	game	NN
en-wikipedia-org-3337	135	37	.	.	.
en-wikipedia-org-3337	136	1	In	in	IN
en-wikipedia-org-3337	136	2	this	this	DT
en-wikipedia-org-3337	136	3	case	case	NN
en-wikipedia-org-3337	136	4	unstable	unstable	JJ
en-wikipedia-org-3337	136	5	equilibria	equilibria	NN
en-wikipedia-org-3337	136	6	are	be	VBP
en-wikipedia-org-3337	136	7	very	very	RB
en-wikipedia-org-3337	136	8	unlikely	unlikely	JJ
en-wikipedia-org-3337	136	9	to	to	TO
en-wikipedia-org-3337	136	10	arise	arise	VB
en-wikipedia-org-3337	136	11	in	in	IN
en-wikipedia-org-3337	136	12	practice	practice	NN
en-wikipedia-org-3337	136	13	,	,	,
en-wikipedia-org-3337	136	14	since	since	IN
en-wikipedia-org-3337	136	15	any	any	DT
en-wikipedia-org-3337	136	16	minute	minute	JJ
en-wikipedia-org-3337	136	17	change	change	NN
en-wikipedia-org-3337	136	18	in	in	IN
en-wikipedia-org-3337	136	19	the	the	DT
en-wikipedia-org-3337	136	20	proportions	proportion	NNS
en-wikipedia-org-3337	136	21	of	of	IN
en-wikipedia-org-3337	136	22	each	each	DT
en-wikipedia-org-3337	136	23	strategy	strategy	NN
en-wikipedia-org-3337	136	24	seen	see	VBN
en-wikipedia-org-3337	136	25	will	will	MD
en-wikipedia-org-3337	136	26	lead	lead	VB
en-wikipedia-org-3337	136	27	to	to	IN
en-wikipedia-org-3337	136	28	a	a	DT
en-wikipedia-org-3337	136	29	change	change	NN
en-wikipedia-org-3337	136	30	in	in	IN
en-wikipedia-org-3337	136	31	strategy	strategy	NN
en-wikipedia-org-3337	136	32	and	and	CC
en-wikipedia-org-3337	136	33	the	the	DT
en-wikipedia-org-3337	136	34	breakdown	breakdown	NN
en-wikipedia-org-3337	136	35	of	of	IN
en-wikipedia-org-3337	136	36	the	the	DT
en-wikipedia-org-3337	136	37	equilibrium	equilibrium	NN
en-wikipedia-org-3337	136	38	.	.	.
en-wikipedia-org-3337	137	1	The	the	DT
en-wikipedia-org-3337	137	2	Nash	Nash	NNP
en-wikipedia-org-3337	137	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	137	4	defines	define	VBZ
en-wikipedia-org-3337	137	5	stability	stability	NN
en-wikipedia-org-3337	137	6	only	only	RB
en-wikipedia-org-3337	137	7	in	in	IN
en-wikipedia-org-3337	137	8	terms	term	NNS
en-wikipedia-org-3337	137	9	of	of	IN
en-wikipedia-org-3337	137	10	unilateral	unilateral	JJ
en-wikipedia-org-3337	137	11	deviations	deviation	NNS
en-wikipedia-org-3337	137	12	.	.	.
en-wikipedia-org-3337	138	1	In	in	IN
en-wikipedia-org-3337	138	2	cooperative	cooperative	JJ
en-wikipedia-org-3337	138	3	games	game	NNS
en-wikipedia-org-3337	138	4	such	such	PDT
en-wikipedia-org-3337	138	5	a	a	DT
en-wikipedia-org-3337	138	6	concept	concept	NN
en-wikipedia-org-3337	138	7	is	be	VBZ
en-wikipedia-org-3337	138	8	not	not	RB
en-wikipedia-org-3337	138	9	convincing	convince	VBG
en-wikipedia-org-3337	138	10	enough	enough	RB
en-wikipedia-org-3337	138	11	.	.	.
en-wikipedia-org-3337	139	1	Strong	strong	JJ
en-wikipedia-org-3337	139	2	Nash	Nash	NNP
en-wikipedia-org-3337	139	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	139	4	allows	allow	VBZ
en-wikipedia-org-3337	139	5	for	for	IN
en-wikipedia-org-3337	139	6	deviations	deviation	NNS
en-wikipedia-org-3337	139	7	by	by	IN
en-wikipedia-org-3337	139	8	every	every	DT
en-wikipedia-org-3337	139	9	conceivable	conceivable	JJ
en-wikipedia-org-3337	139	10	coalition	coalition	NN
en-wikipedia-org-3337	139	11	.	.	.
en-wikipedia-org-3337	140	1	[	[	-LRB-
en-wikipedia-org-3337	140	2	17	17	CD
en-wikipedia-org-3337	140	3	]	]	-RRB-
en-wikipedia-org-3337	140	4	Formally	formally	RB
en-wikipedia-org-3337	140	5	,	,	,
en-wikipedia-org-3337	140	6	a	a	DT
en-wikipedia-org-3337	140	7	strong	strong	JJ
en-wikipedia-org-3337	140	8	Nash	Nash	NNP
en-wikipedia-org-3337	140	9	equilibrium	equilibrium	NN
en-wikipedia-org-3337	140	10	is	be	VBZ
en-wikipedia-org-3337	140	11	a	a	DT
en-wikipedia-org-3337	140	12	Nash	Nash	NNP
en-wikipedia-org-3337	140	13	equilibrium	equilibrium	NN
en-wikipedia-org-3337	140	14	in	in	IN
en-wikipedia-org-3337	140	15	which	which	WDT
en-wikipedia-org-3337	140	16	no	no	DT
en-wikipedia-org-3337	140	17	coalition	coalition	NN
en-wikipedia-org-3337	140	18	,	,	,
en-wikipedia-org-3337	140	19	taking	take	VBG
en-wikipedia-org-3337	140	20	the	the	DT
en-wikipedia-org-3337	140	21	actions	action	NNS
en-wikipedia-org-3337	140	22	of	of	IN
en-wikipedia-org-3337	140	23	its	-PRON-	PRP$
en-wikipedia-org-3337	140	24	complements	complement	NNS
en-wikipedia-org-3337	140	25	as	as	IN
en-wikipedia-org-3337	140	26	given	give	VBN
en-wikipedia-org-3337	140	27	,	,	,
en-wikipedia-org-3337	140	28	can	can	MD
en-wikipedia-org-3337	140	29	cooperatively	cooperatively	RB
en-wikipedia-org-3337	140	30	deviate	deviate	VB
en-wikipedia-org-3337	140	31	in	in	IN
en-wikipedia-org-3337	140	32	a	a	DT
en-wikipedia-org-3337	140	33	way	way	NN
en-wikipedia-org-3337	140	34	that	that	WDT
en-wikipedia-org-3337	140	35	benefits	benefit	VBZ
en-wikipedia-org-3337	140	36	all	all	DT
en-wikipedia-org-3337	140	37	of	of	IN
en-wikipedia-org-3337	140	38	its	-PRON-	PRP$
en-wikipedia-org-3337	140	39	members	member	NNS
en-wikipedia-org-3337	140	40	.	.	.
en-wikipedia-org-3337	141	1	[	[	-LRB-
en-wikipedia-org-3337	141	2	18	18	CD
en-wikipedia-org-3337	141	3	]	]	-RRB-
en-wikipedia-org-3337	141	4	However	however	RB
en-wikipedia-org-3337	141	5	,	,	,
en-wikipedia-org-3337	141	6	the	the	DT
en-wikipedia-org-3337	141	7	strong	strong	JJ
en-wikipedia-org-3337	141	8	Nash	Nash	NNP
en-wikipedia-org-3337	141	9	concept	concept	NN
en-wikipedia-org-3337	141	10	is	be	VBZ
en-wikipedia-org-3337	141	11	sometimes	sometimes	RB
en-wikipedia-org-3337	141	12	perceived	perceive	VBN
en-wikipedia-org-3337	141	13	as	as	IN
en-wikipedia-org-3337	141	14	too	too	RB
en-wikipedia-org-3337	141	15	"	"	``
en-wikipedia-org-3337	141	16	strong	strong	JJ
en-wikipedia-org-3337	141	17	"	"	''
en-wikipedia-org-3337	141	18	in	in	IN
en-wikipedia-org-3337	141	19	that	that	IN
en-wikipedia-org-3337	141	20	the	the	DT
en-wikipedia-org-3337	141	21	environment	environment	NN
en-wikipedia-org-3337	141	22	allows	allow	VBZ
en-wikipedia-org-3337	141	23	for	for	IN
en-wikipedia-org-3337	141	24	unlimited	unlimited	JJ
en-wikipedia-org-3337	141	25	private	private	JJ
en-wikipedia-org-3337	141	26	communication	communication	NN
en-wikipedia-org-3337	141	27	.	.	.
en-wikipedia-org-3337	142	1	In	in	IN
en-wikipedia-org-3337	142	2	fact	fact	NN
en-wikipedia-org-3337	142	3	,	,	,
en-wikipedia-org-3337	142	4	strong	strong	JJ
en-wikipedia-org-3337	142	5	Nash	Nash	NNP
en-wikipedia-org-3337	142	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	142	7	has	have	VBZ
en-wikipedia-org-3337	142	8	to	to	TO
en-wikipedia-org-3337	142	9	be	be	VB
en-wikipedia-org-3337	142	10	Pareto	Pareto	NNP
en-wikipedia-org-3337	142	11	efficient	efficient	JJ
en-wikipedia-org-3337	142	12	.	.	.
en-wikipedia-org-3337	143	1	As	as	IN
en-wikipedia-org-3337	143	2	a	a	DT
en-wikipedia-org-3337	143	3	result	result	NN
en-wikipedia-org-3337	143	4	of	of	IN
en-wikipedia-org-3337	143	5	these	these	DT
en-wikipedia-org-3337	143	6	requirements	requirement	NNS
en-wikipedia-org-3337	143	7	,	,	,
en-wikipedia-org-3337	143	8	strong	strong	JJ
en-wikipedia-org-3337	143	9	Nash	Nash	NNP
en-wikipedia-org-3337	143	10	is	be	VBZ
en-wikipedia-org-3337	143	11	too	too	RB
en-wikipedia-org-3337	143	12	rare	rare	JJ
en-wikipedia-org-3337	143	13	to	to	TO
en-wikipedia-org-3337	143	14	be	be	VB
en-wikipedia-org-3337	143	15	useful	useful	JJ
en-wikipedia-org-3337	143	16	in	in	IN
en-wikipedia-org-3337	143	17	many	many	JJ
en-wikipedia-org-3337	143	18	branches	branch	NNS
en-wikipedia-org-3337	143	19	of	of	IN
en-wikipedia-org-3337	143	20	game	game	NN
en-wikipedia-org-3337	143	21	theory	theory	NN
en-wikipedia-org-3337	143	22	.	.	.
en-wikipedia-org-3337	144	1	However	however	RB
en-wikipedia-org-3337	144	2	,	,	,
en-wikipedia-org-3337	144	3	in	in	IN
en-wikipedia-org-3337	144	4	games	game	NNS
en-wikipedia-org-3337	144	5	such	such	JJ
en-wikipedia-org-3337	144	6	as	as	IN
en-wikipedia-org-3337	144	7	elections	election	NNS
en-wikipedia-org-3337	144	8	with	with	IN
en-wikipedia-org-3337	144	9	many	many	JJ
en-wikipedia-org-3337	144	10	more	more	JJR
en-wikipedia-org-3337	144	11	players	player	NNS
en-wikipedia-org-3337	144	12	than	than	IN
en-wikipedia-org-3337	144	13	possible	possible	JJ
en-wikipedia-org-3337	144	14	outcomes	outcome	NNS
en-wikipedia-org-3337	144	15	,	,	,
en-wikipedia-org-3337	144	16	it	-PRON-	PRP
en-wikipedia-org-3337	144	17	can	can	MD
en-wikipedia-org-3337	144	18	be	be	VB
en-wikipedia-org-3337	144	19	more	more	RBR
en-wikipedia-org-3337	144	20	common	common	JJ
en-wikipedia-org-3337	144	21	than	than	IN
en-wikipedia-org-3337	144	22	a	a	DT
en-wikipedia-org-3337	144	23	stable	stable	JJ
en-wikipedia-org-3337	144	24	equilibrium	equilibrium	NN
en-wikipedia-org-3337	144	25	.	.	.
en-wikipedia-org-3337	145	1	A	a	DT
en-wikipedia-org-3337	145	2	refined	refined	JJ
en-wikipedia-org-3337	145	3	Nash	Nash	NNP
en-wikipedia-org-3337	145	4	equilibrium	equilibrium	NN
en-wikipedia-org-3337	145	5	known	know	VBN
en-wikipedia-org-3337	145	6	as	as	IN
en-wikipedia-org-3337	145	7	coalition	coalition	NN
en-wikipedia-org-3337	145	8	-	-	HYPH
en-wikipedia-org-3337	145	9	proof	proof	JJ
en-wikipedia-org-3337	145	10	Nash	Nash	NNP
en-wikipedia-org-3337	145	11	equilibrium	equilibrium	NN
en-wikipedia-org-3337	145	12	(	(	-LRB-
en-wikipedia-org-3337	145	13	CPNE)[17	CPNE)[17	NNP
en-wikipedia-org-3337	145	14	]	]	-RRB-
en-wikipedia-org-3337	145	15	occurs	occur	VBZ
en-wikipedia-org-3337	145	16	when	when	WRB
en-wikipedia-org-3337	145	17	players	player	NNS
en-wikipedia-org-3337	145	18	can	can	MD
en-wikipedia-org-3337	145	19	not	not	RB
en-wikipedia-org-3337	145	20	do	do	VB
en-wikipedia-org-3337	145	21	better	well	RBR
en-wikipedia-org-3337	145	22	even	even	RB
en-wikipedia-org-3337	145	23	if	if	IN
en-wikipedia-org-3337	145	24	they	-PRON-	PRP
en-wikipedia-org-3337	145	25	are	be	VBP
en-wikipedia-org-3337	145	26	allowed	allow	VBN
en-wikipedia-org-3337	145	27	to	to	TO
en-wikipedia-org-3337	145	28	communicate	communicate	VB
en-wikipedia-org-3337	145	29	and	and	CC
en-wikipedia-org-3337	145	30	make	make	VB
en-wikipedia-org-3337	145	31	"	"	``
en-wikipedia-org-3337	145	32	self	self	NN
en-wikipedia-org-3337	145	33	-	-	HYPH
en-wikipedia-org-3337	145	34	enforcing	enforce	VBG
en-wikipedia-org-3337	145	35	"	"	''
en-wikipedia-org-3337	145	36	agreement	agreement	NN
en-wikipedia-org-3337	145	37	to	to	TO
en-wikipedia-org-3337	145	38	deviate	deviate	VB
en-wikipedia-org-3337	145	39	.	.	.
en-wikipedia-org-3337	146	1	Every	every	DT
en-wikipedia-org-3337	146	2	correlated	correlate	VBN
en-wikipedia-org-3337	146	3	strategy	strategy	NN
en-wikipedia-org-3337	146	4	supported	support	VBN
en-wikipedia-org-3337	146	5	by	by	IN
en-wikipedia-org-3337	146	6	iterated	iterated	JJ
en-wikipedia-org-3337	146	7	strict	strict	JJ
en-wikipedia-org-3337	146	8	dominance	dominance	NN
en-wikipedia-org-3337	146	9	and	and	CC
en-wikipedia-org-3337	146	10	on	on	IN
en-wikipedia-org-3337	146	11	the	the	DT
en-wikipedia-org-3337	146	12	Pareto	Pareto	NNP
en-wikipedia-org-3337	146	13	frontier	frontier	NN
en-wikipedia-org-3337	146	14	is	be	VBZ
en-wikipedia-org-3337	146	15	a	a	DT
en-wikipedia-org-3337	146	16	CPNE	CPNE	NNP
en-wikipedia-org-3337	146	17	.	.	.
en-wikipedia-org-3337	147	1	[	[	-LRB-
en-wikipedia-org-3337	147	2	19	19	CD
en-wikipedia-org-3337	147	3	]	]	-RRB-
en-wikipedia-org-3337	147	4	Further	further	RB
en-wikipedia-org-3337	147	5	,	,	,
en-wikipedia-org-3337	147	6	it	-PRON-	PRP
en-wikipedia-org-3337	147	7	is	be	VBZ
en-wikipedia-org-3337	147	8	possible	possible	JJ
en-wikipedia-org-3337	147	9	for	for	IN
en-wikipedia-org-3337	147	10	a	a	DT
en-wikipedia-org-3337	147	11	game	game	NN
en-wikipedia-org-3337	147	12	to	to	TO
en-wikipedia-org-3337	147	13	have	have	VB
en-wikipedia-org-3337	147	14	a	a	DT
en-wikipedia-org-3337	147	15	Nash	Nash	NNP
en-wikipedia-org-3337	147	16	equilibrium	equilibrium	NN
en-wikipedia-org-3337	147	17	that	that	WDT
en-wikipedia-org-3337	147	18	is	be	VBZ
en-wikipedia-org-3337	147	19	resilient	resilient	JJ
en-wikipedia-org-3337	147	20	against	against	IN
en-wikipedia-org-3337	147	21	coalitions	coalition	NNS
en-wikipedia-org-3337	147	22	less	less	JJR
en-wikipedia-org-3337	147	23	than	than	IN
en-wikipedia-org-3337	147	24	a	a	DT
en-wikipedia-org-3337	147	25	specified	specify	VBN
en-wikipedia-org-3337	147	26	size	size	NN
en-wikipedia-org-3337	147	27	,	,	,
en-wikipedia-org-3337	147	28	k.	k.	NN
en-wikipedia-org-3337	147	29	CPNE	CPNE	NNP
en-wikipedia-org-3337	147	30	is	be	VBZ
en-wikipedia-org-3337	147	31	related	relate	VBN
en-wikipedia-org-3337	147	32	to	to	IN
en-wikipedia-org-3337	147	33	the	the	DT
en-wikipedia-org-3337	147	34	theory	theory	NN
en-wikipedia-org-3337	147	35	of	of	IN
en-wikipedia-org-3337	147	36	the	the	DT
en-wikipedia-org-3337	147	37	core	core	NN
en-wikipedia-org-3337	147	38	.	.	.
en-wikipedia-org-3337	148	1	Finally	finally	RB
en-wikipedia-org-3337	148	2	in	in	IN
en-wikipedia-org-3337	148	3	the	the	DT
en-wikipedia-org-3337	148	4	eighties	eighty	NNS
en-wikipedia-org-3337	148	5	,	,	,
en-wikipedia-org-3337	148	6	building	build	VBG
en-wikipedia-org-3337	148	7	with	with	IN
en-wikipedia-org-3337	148	8	great	great	JJ
en-wikipedia-org-3337	148	9	depth	depth	NN
en-wikipedia-org-3337	148	10	on	on	IN
en-wikipedia-org-3337	148	11	such	such	JJ
en-wikipedia-org-3337	148	12	ideas	idea	NNS
en-wikipedia-org-3337	148	13	Mertens	Mertens	NNP
en-wikipedia-org-3337	148	14	-	-	HYPH
en-wikipedia-org-3337	148	15	stable	stable	JJ
en-wikipedia-org-3337	148	16	equilibria	equilibrium	NNS
en-wikipedia-org-3337	148	17	were	be	VBD
en-wikipedia-org-3337	148	18	introduced	introduce	VBN
en-wikipedia-org-3337	148	19	as	as	IN
en-wikipedia-org-3337	148	20	a	a	DT
en-wikipedia-org-3337	148	21	solution	solution	NN
en-wikipedia-org-3337	148	22	concept	concept	NN
en-wikipedia-org-3337	148	23	.	.	.
en-wikipedia-org-3337	149	1	Mertens	Mertens	NNP
en-wikipedia-org-3337	149	2	stable	stable	JJ
en-wikipedia-org-3337	149	3	equilibria	equilibrium	NNS
en-wikipedia-org-3337	149	4	satisfy	satisfy	VBP
en-wikipedia-org-3337	149	5	both	both	CC
en-wikipedia-org-3337	149	6	forward	forward	RB
en-wikipedia-org-3337	149	7	induction	induction	NN
en-wikipedia-org-3337	149	8	and	and	CC
en-wikipedia-org-3337	149	9	backward	backward	JJ
en-wikipedia-org-3337	149	10	induction	induction	NN
en-wikipedia-org-3337	149	11	.	.	.
en-wikipedia-org-3337	150	1	In	in	IN
en-wikipedia-org-3337	150	2	a	a	DT
en-wikipedia-org-3337	150	3	game	game	NN
en-wikipedia-org-3337	150	4	theory	theory	NN
en-wikipedia-org-3337	150	5	context	context	NN
en-wikipedia-org-3337	150	6	stable	stable	JJ
en-wikipedia-org-3337	150	7	equilibria	equilibrium	NNS
en-wikipedia-org-3337	150	8	now	now	RB
en-wikipedia-org-3337	150	9	usually	usually	RB
en-wikipedia-org-3337	150	10	refer	refer	VBP
en-wikipedia-org-3337	150	11	to	to	IN
en-wikipedia-org-3337	150	12	Mertens	Mertens	NNP
en-wikipedia-org-3337	150	13	stable	stable	JJ
en-wikipedia-org-3337	150	14	equilibria	equilibria	NN
en-wikipedia-org-3337	150	15	.	.	.
en-wikipedia-org-3337	151	1	Occurrence[edit	occurrence[edit	LS
en-wikipedia-org-3337	151	2	]	]	-RRB-
en-wikipedia-org-3337	151	3	If	if	IN
en-wikipedia-org-3337	151	4	a	a	DT
en-wikipedia-org-3337	151	5	game	game	NN
en-wikipedia-org-3337	151	6	has	have	VBZ
en-wikipedia-org-3337	151	7	a	a	DT
en-wikipedia-org-3337	151	8	unique	unique	JJ
en-wikipedia-org-3337	151	9	Nash	Nash	NNP
en-wikipedia-org-3337	151	10	equilibrium	equilibrium	NN
en-wikipedia-org-3337	151	11	and	and	CC
en-wikipedia-org-3337	151	12	is	be	VBZ
en-wikipedia-org-3337	151	13	played	play	VBN
en-wikipedia-org-3337	151	14	among	among	IN
en-wikipedia-org-3337	151	15	players	player	NNS
en-wikipedia-org-3337	151	16	under	under	IN
en-wikipedia-org-3337	151	17	certain	certain	JJ
en-wikipedia-org-3337	151	18	conditions	condition	NNS
en-wikipedia-org-3337	151	19	,	,	,
en-wikipedia-org-3337	151	20	then	then	RB
en-wikipedia-org-3337	151	21	the	the	DT
en-wikipedia-org-3337	151	22	NE	NE	NNP
en-wikipedia-org-3337	151	23	strategy	strategy	NN
en-wikipedia-org-3337	151	24	set	set	NN
en-wikipedia-org-3337	151	25	will	will	MD
en-wikipedia-org-3337	151	26	be	be	VB
en-wikipedia-org-3337	151	27	adopted	adopt	VBN
en-wikipedia-org-3337	151	28	.	.	.
en-wikipedia-org-3337	152	1	Sufficient	sufficient	JJ
en-wikipedia-org-3337	152	2	conditions	condition	NNS
en-wikipedia-org-3337	152	3	to	to	TO
en-wikipedia-org-3337	152	4	guarantee	guarantee	VB
en-wikipedia-org-3337	152	5	that	that	IN
en-wikipedia-org-3337	152	6	the	the	DT
en-wikipedia-org-3337	152	7	Nash	Nash	NNP
en-wikipedia-org-3337	152	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	152	9	is	be	VBZ
en-wikipedia-org-3337	152	10	played	play	VBN
en-wikipedia-org-3337	152	11	are	be	VBP
en-wikipedia-org-3337	152	12	:	:	:
en-wikipedia-org-3337	152	13	The	the	DT
en-wikipedia-org-3337	152	14	players	player	NNS
en-wikipedia-org-3337	152	15	all	all	DT
en-wikipedia-org-3337	152	16	will	will	MD
en-wikipedia-org-3337	152	17	do	do	VB
en-wikipedia-org-3337	152	18	their	-PRON-	PRP$
en-wikipedia-org-3337	152	19	utmost	utmost	NN
en-wikipedia-org-3337	152	20	to	to	TO
en-wikipedia-org-3337	152	21	maximize	maximize	VB
en-wikipedia-org-3337	152	22	their	-PRON-	PRP$
en-wikipedia-org-3337	152	23	expected	expect	VBN
en-wikipedia-org-3337	152	24	payoff	payoff	NN
en-wikipedia-org-3337	152	25	as	as	IN
en-wikipedia-org-3337	152	26	described	describe	VBN
en-wikipedia-org-3337	152	27	by	by	IN
en-wikipedia-org-3337	152	28	the	the	DT
en-wikipedia-org-3337	152	29	game	game	NN
en-wikipedia-org-3337	152	30	.	.	.
en-wikipedia-org-3337	153	1	The	the	DT
en-wikipedia-org-3337	153	2	players	player	NNS
en-wikipedia-org-3337	153	3	are	be	VBP
en-wikipedia-org-3337	153	4	flawless	flawless	JJ
en-wikipedia-org-3337	153	5	in	in	IN
en-wikipedia-org-3337	153	6	execution	execution	NN
en-wikipedia-org-3337	153	7	.	.	.
en-wikipedia-org-3337	154	1	The	the	DT
en-wikipedia-org-3337	154	2	players	player	NNS
en-wikipedia-org-3337	154	3	have	have	VBP
en-wikipedia-org-3337	154	4	sufficient	sufficient	JJ
en-wikipedia-org-3337	154	5	intelligence	intelligence	NN
en-wikipedia-org-3337	154	6	to	to	TO
en-wikipedia-org-3337	154	7	deduce	deduce	VB
en-wikipedia-org-3337	154	8	the	the	DT
en-wikipedia-org-3337	154	9	solution	solution	NN
en-wikipedia-org-3337	154	10	.	.	.
en-wikipedia-org-3337	155	1	The	the	DT
en-wikipedia-org-3337	155	2	players	player	NNS
en-wikipedia-org-3337	155	3	know	know	VBP
en-wikipedia-org-3337	155	4	the	the	DT
en-wikipedia-org-3337	155	5	planned	plan	VBN
en-wikipedia-org-3337	155	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	155	7	strategy	strategy	NN
en-wikipedia-org-3337	155	8	of	of	IN
en-wikipedia-org-3337	155	9	all	all	DT
en-wikipedia-org-3337	155	10	of	of	IN
en-wikipedia-org-3337	155	11	the	the	DT
en-wikipedia-org-3337	155	12	other	other	JJ
en-wikipedia-org-3337	155	13	players	player	NNS
en-wikipedia-org-3337	155	14	.	.	.
en-wikipedia-org-3337	156	1	The	the	DT
en-wikipedia-org-3337	156	2	players	player	NNS
en-wikipedia-org-3337	156	3	believe	believe	VBP
en-wikipedia-org-3337	156	4	that	that	IN
en-wikipedia-org-3337	156	5	a	a	DT
en-wikipedia-org-3337	156	6	deviation	deviation	NN
en-wikipedia-org-3337	156	7	in	in	IN
en-wikipedia-org-3337	156	8	their	-PRON-	PRP$
en-wikipedia-org-3337	156	9	own	own	JJ
en-wikipedia-org-3337	156	10	strategy	strategy	NN
en-wikipedia-org-3337	156	11	will	will	MD
en-wikipedia-org-3337	156	12	not	not	RB
en-wikipedia-org-3337	156	13	cause	cause	VB
en-wikipedia-org-3337	156	14	deviations	deviation	NNS
en-wikipedia-org-3337	156	15	by	by	IN
en-wikipedia-org-3337	156	16	any	any	DT
en-wikipedia-org-3337	156	17	other	other	JJ
en-wikipedia-org-3337	156	18	players	player	NNS
en-wikipedia-org-3337	156	19	.	.	.
en-wikipedia-org-3337	157	1	There	there	EX
en-wikipedia-org-3337	157	2	is	be	VBZ
en-wikipedia-org-3337	157	3	common	common	JJ
en-wikipedia-org-3337	157	4	knowledge	knowledge	NN
en-wikipedia-org-3337	157	5	that	that	IN
en-wikipedia-org-3337	157	6	all	all	DT
en-wikipedia-org-3337	157	7	players	player	NNS
en-wikipedia-org-3337	157	8	meet	meet	VBP
en-wikipedia-org-3337	157	9	these	these	DT
en-wikipedia-org-3337	157	10	conditions	condition	NNS
en-wikipedia-org-3337	157	11	,	,	,
en-wikipedia-org-3337	157	12	including	include	VBG
en-wikipedia-org-3337	157	13	this	this	DT
en-wikipedia-org-3337	157	14	one	one	NN
en-wikipedia-org-3337	157	15	.	.	.
en-wikipedia-org-3337	158	1	So	so	CC
en-wikipedia-org-3337	158	2	,	,	,
en-wikipedia-org-3337	158	3	not	not	RB
en-wikipedia-org-3337	158	4	only	only	RB
en-wikipedia-org-3337	158	5	must	must	MD
en-wikipedia-org-3337	158	6	each	each	DT
en-wikipedia-org-3337	158	7	player	player	NN
en-wikipedia-org-3337	158	8	know	know	VB
en-wikipedia-org-3337	158	9	the	the	DT
en-wikipedia-org-3337	158	10	other	other	JJ
en-wikipedia-org-3337	158	11	players	player	NNS
en-wikipedia-org-3337	158	12	meet	meet	VBP
en-wikipedia-org-3337	158	13	the	the	DT
en-wikipedia-org-3337	158	14	conditions	condition	NNS
en-wikipedia-org-3337	158	15	,	,	,
en-wikipedia-org-3337	158	16	but	but	CC
en-wikipedia-org-3337	158	17	also	also	RB
en-wikipedia-org-3337	158	18	they	-PRON-	PRP
en-wikipedia-org-3337	158	19	must	must	MD
en-wikipedia-org-3337	158	20	know	know	VB
en-wikipedia-org-3337	158	21	that	that	IN
en-wikipedia-org-3337	158	22	they	-PRON-	PRP
en-wikipedia-org-3337	158	23	all	all	DT
en-wikipedia-org-3337	158	24	know	know	VBP
en-wikipedia-org-3337	158	25	that	that	IN
en-wikipedia-org-3337	158	26	they	-PRON-	PRP
en-wikipedia-org-3337	158	27	meet	meet	VBP
en-wikipedia-org-3337	158	28	them	-PRON-	PRP
en-wikipedia-org-3337	158	29	,	,	,
en-wikipedia-org-3337	158	30	and	and	CC
en-wikipedia-org-3337	158	31	know	know	VBP
en-wikipedia-org-3337	158	32	that	that	IN
en-wikipedia-org-3337	158	33	they	-PRON-	PRP
en-wikipedia-org-3337	158	34	know	know	VBP
en-wikipedia-org-3337	158	35	that	that	IN
en-wikipedia-org-3337	158	36	they	-PRON-	PRP
en-wikipedia-org-3337	158	37	know	know	VBP
en-wikipedia-org-3337	158	38	that	that	IN
en-wikipedia-org-3337	158	39	they	-PRON-	PRP
en-wikipedia-org-3337	158	40	meet	meet	VBP
en-wikipedia-org-3337	158	41	them	-PRON-	PRP
en-wikipedia-org-3337	158	42	,	,	,
en-wikipedia-org-3337	158	43	and	and	CC
en-wikipedia-org-3337	158	44	so	so	RB
en-wikipedia-org-3337	158	45	on	on	RB
en-wikipedia-org-3337	158	46	.	.	.
en-wikipedia-org-3337	159	1	Where	where	WRB
en-wikipedia-org-3337	159	2	the	the	DT
en-wikipedia-org-3337	159	3	conditions	condition	NNS
en-wikipedia-org-3337	159	4	are	be	VBP
en-wikipedia-org-3337	159	5	not	not	RB
en-wikipedia-org-3337	159	6	met[edit	met[edit	VBG
en-wikipedia-org-3337	159	7	]	]	-RRB-
en-wikipedia-org-3337	159	8	Examples	example	NNS
en-wikipedia-org-3337	159	9	of	of	IN
en-wikipedia-org-3337	159	10	game	game	NN
en-wikipedia-org-3337	159	11	theory	theory	NN
en-wikipedia-org-3337	159	12	problems	problem	NNS
en-wikipedia-org-3337	159	13	in	in	IN
en-wikipedia-org-3337	159	14	which	which	WDT
en-wikipedia-org-3337	159	15	these	these	DT
en-wikipedia-org-3337	159	16	conditions	condition	NNS
en-wikipedia-org-3337	159	17	are	be	VBP
en-wikipedia-org-3337	159	18	not	not	RB
en-wikipedia-org-3337	159	19	met	meet	VBN
en-wikipedia-org-3337	159	20	:	:	:
en-wikipedia-org-3337	159	21	The	the	DT
en-wikipedia-org-3337	159	22	first	first	JJ
en-wikipedia-org-3337	159	23	condition	condition	NN
en-wikipedia-org-3337	159	24	is	be	VBZ
en-wikipedia-org-3337	159	25	not	not	RB
en-wikipedia-org-3337	159	26	met	meet	VBN
en-wikipedia-org-3337	159	27	if	if	IN
en-wikipedia-org-3337	159	28	the	the	DT
en-wikipedia-org-3337	159	29	game	game	NN
en-wikipedia-org-3337	159	30	does	do	VBZ
en-wikipedia-org-3337	159	31	not	not	RB
en-wikipedia-org-3337	159	32	correctly	correctly	RB
en-wikipedia-org-3337	159	33	describe	describe	VB
en-wikipedia-org-3337	159	34	the	the	DT
en-wikipedia-org-3337	159	35	quantities	quantity	NNS
en-wikipedia-org-3337	159	36	a	a	DT
en-wikipedia-org-3337	159	37	player	player	NN
en-wikipedia-org-3337	159	38	wishes	wish	VBZ
en-wikipedia-org-3337	159	39	to	to	TO
en-wikipedia-org-3337	159	40	maximize	maximize	VB
en-wikipedia-org-3337	159	41	.	.	.
en-wikipedia-org-3337	160	1	In	in	IN
en-wikipedia-org-3337	160	2	this	this	DT
en-wikipedia-org-3337	160	3	case	case	NN
en-wikipedia-org-3337	160	4	there	there	EX
en-wikipedia-org-3337	160	5	is	be	VBZ
en-wikipedia-org-3337	160	6	no	no	DT
en-wikipedia-org-3337	160	7	particular	particular	JJ
en-wikipedia-org-3337	160	8	reason	reason	NN
en-wikipedia-org-3337	160	9	for	for	IN
en-wikipedia-org-3337	160	10	that	that	DT
en-wikipedia-org-3337	160	11	player	player	NN
en-wikipedia-org-3337	160	12	to	to	TO
en-wikipedia-org-3337	160	13	adopt	adopt	VB
en-wikipedia-org-3337	160	14	an	an	DT
en-wikipedia-org-3337	160	15	equilibrium	equilibrium	NN
en-wikipedia-org-3337	160	16	strategy	strategy	NN
en-wikipedia-org-3337	160	17	.	.	.
en-wikipedia-org-3337	161	1	For	for	IN
en-wikipedia-org-3337	161	2	instance	instance	NN
en-wikipedia-org-3337	161	3	,	,	,
en-wikipedia-org-3337	161	4	the	the	DT
en-wikipedia-org-3337	161	5	prisoner	prisoner	NN
en-wikipedia-org-3337	161	6	's	's	POS
en-wikipedia-org-3337	161	7	dilemma	dilemma	NN
en-wikipedia-org-3337	161	8	is	be	VBZ
en-wikipedia-org-3337	161	9	not	not	RB
en-wikipedia-org-3337	161	10	a	a	DT
en-wikipedia-org-3337	161	11	dilemma	dilemma	NN
en-wikipedia-org-3337	161	12	if	if	IN
en-wikipedia-org-3337	161	13	either	either	DT
en-wikipedia-org-3337	161	14	player	player	NN
en-wikipedia-org-3337	161	15	is	be	VBZ
en-wikipedia-org-3337	161	16	happy	happy	JJ
en-wikipedia-org-3337	161	17	to	to	TO
en-wikipedia-org-3337	161	18	be	be	VB
en-wikipedia-org-3337	161	19	jailed	jail	VBN
en-wikipedia-org-3337	161	20	indefinitely	indefinitely	RB
en-wikipedia-org-3337	161	21	.	.	.
en-wikipedia-org-3337	162	1	Intentional	intentional	JJ
en-wikipedia-org-3337	162	2	or	or	CC
en-wikipedia-org-3337	162	3	accidental	accidental	JJ
en-wikipedia-org-3337	162	4	imperfection	imperfection	NN
en-wikipedia-org-3337	162	5	in	in	IN
en-wikipedia-org-3337	162	6	execution	execution	NN
en-wikipedia-org-3337	162	7	.	.	.
en-wikipedia-org-3337	163	1	For	for	IN
en-wikipedia-org-3337	163	2	example	example	NN
en-wikipedia-org-3337	163	3	,	,	,
en-wikipedia-org-3337	163	4	a	a	DT
en-wikipedia-org-3337	163	5	computer	computer	NN
en-wikipedia-org-3337	163	6	capable	capable	JJ
en-wikipedia-org-3337	163	7	of	of	IN
en-wikipedia-org-3337	163	8	flawless	flawless	JJ
en-wikipedia-org-3337	163	9	logical	logical	JJ
en-wikipedia-org-3337	163	10	play	play	NN
en-wikipedia-org-3337	163	11	facing	face	VBG
en-wikipedia-org-3337	163	12	a	a	DT
en-wikipedia-org-3337	163	13	second	second	JJ
en-wikipedia-org-3337	163	14	flawless	flawless	JJ
en-wikipedia-org-3337	163	15	computer	computer	NN
en-wikipedia-org-3337	163	16	will	will	MD
en-wikipedia-org-3337	163	17	result	result	VB
en-wikipedia-org-3337	163	18	in	in	IN
en-wikipedia-org-3337	163	19	equilibrium	equilibrium	NN
en-wikipedia-org-3337	163	20	.	.	.
en-wikipedia-org-3337	164	1	Introduction	introduction	NN
en-wikipedia-org-3337	164	2	of	of	IN
en-wikipedia-org-3337	164	3	imperfection	imperfection	NN
en-wikipedia-org-3337	164	4	will	will	MD
en-wikipedia-org-3337	164	5	lead	lead	VB
en-wikipedia-org-3337	164	6	to	to	IN
en-wikipedia-org-3337	164	7	its	-PRON-	PRP$
en-wikipedia-org-3337	164	8	disruption	disruption	NN
en-wikipedia-org-3337	164	9	either	either	CC
en-wikipedia-org-3337	164	10	through	through	IN
en-wikipedia-org-3337	164	11	loss	loss	NN
en-wikipedia-org-3337	164	12	to	to	IN
en-wikipedia-org-3337	164	13	the	the	DT
en-wikipedia-org-3337	164	14	player	player	NN
en-wikipedia-org-3337	164	15	who	who	WP
en-wikipedia-org-3337	164	16	makes	make	VBZ
en-wikipedia-org-3337	164	17	the	the	DT
en-wikipedia-org-3337	164	18	mistake	mistake	NN
en-wikipedia-org-3337	164	19	,	,	,
en-wikipedia-org-3337	164	20	or	or	CC
en-wikipedia-org-3337	164	21	through	through	IN
en-wikipedia-org-3337	164	22	negation	negation	NN
en-wikipedia-org-3337	164	23	of	of	IN
en-wikipedia-org-3337	164	24	the	the	DT
en-wikipedia-org-3337	164	25	common	common	JJ
en-wikipedia-org-3337	164	26	knowledge	knowledge	NN
en-wikipedia-org-3337	164	27	criterion	criterion	NN
en-wikipedia-org-3337	164	28	leading	lead	VBG
en-wikipedia-org-3337	164	29	to	to	IN
en-wikipedia-org-3337	164	30	possible	possible	JJ
en-wikipedia-org-3337	164	31	victory	victory	NN
en-wikipedia-org-3337	164	32	for	for	IN
en-wikipedia-org-3337	164	33	the	the	DT
en-wikipedia-org-3337	164	34	player	player	NN
en-wikipedia-org-3337	164	35	.	.	.
en-wikipedia-org-3337	165	1	(	(	-LRB-
en-wikipedia-org-3337	165	2	An	an	DT
en-wikipedia-org-3337	165	3	example	example	NN
en-wikipedia-org-3337	165	4	would	would	MD
en-wikipedia-org-3337	165	5	be	be	VB
en-wikipedia-org-3337	165	6	a	a	DT
en-wikipedia-org-3337	165	7	player	player	NN
en-wikipedia-org-3337	165	8	suddenly	suddenly	RB
en-wikipedia-org-3337	165	9	putting	put	VBG
en-wikipedia-org-3337	165	10	the	the	DT
en-wikipedia-org-3337	165	11	car	car	NN
en-wikipedia-org-3337	165	12	into	into	IN
en-wikipedia-org-3337	165	13	reverse	reverse	NN
en-wikipedia-org-3337	165	14	in	in	IN
en-wikipedia-org-3337	165	15	the	the	DT
en-wikipedia-org-3337	165	16	game	game	NN
en-wikipedia-org-3337	165	17	of	of	IN
en-wikipedia-org-3337	165	18	chicken	chicken	NN
en-wikipedia-org-3337	165	19	,	,	,
en-wikipedia-org-3337	165	20	ensuring	ensure	VBG
en-wikipedia-org-3337	165	21	a	a	DT
en-wikipedia-org-3337	165	22	no	no	DT
en-wikipedia-org-3337	165	23	-	-	HYPH
en-wikipedia-org-3337	165	24	loss	loss	NN
en-wikipedia-org-3337	165	25	no	no	DT
en-wikipedia-org-3337	165	26	-	-	HYPH
en-wikipedia-org-3337	165	27	win	win	NN
en-wikipedia-org-3337	165	28	scenario	scenario	NN
en-wikipedia-org-3337	165	29	)	)	-RRB-
en-wikipedia-org-3337	165	30	.	.	.
en-wikipedia-org-3337	166	1	In	in	IN
en-wikipedia-org-3337	166	2	many	many	JJ
en-wikipedia-org-3337	166	3	cases	case	NNS
en-wikipedia-org-3337	166	4	,	,	,
en-wikipedia-org-3337	166	5	the	the	DT
en-wikipedia-org-3337	166	6	third	third	JJ
en-wikipedia-org-3337	166	7	condition	condition	NN
en-wikipedia-org-3337	166	8	is	be	VBZ
en-wikipedia-org-3337	166	9	not	not	RB
en-wikipedia-org-3337	166	10	met	meet	VBN
en-wikipedia-org-3337	166	11	because	because	IN
en-wikipedia-org-3337	166	12	,	,	,
en-wikipedia-org-3337	166	13	even	even	RB
en-wikipedia-org-3337	166	14	though	though	IN
en-wikipedia-org-3337	166	15	the	the	DT
en-wikipedia-org-3337	166	16	equilibrium	equilibrium	NN
en-wikipedia-org-3337	166	17	must	must	MD
en-wikipedia-org-3337	166	18	exist	exist	VB
en-wikipedia-org-3337	166	19	,	,	,
en-wikipedia-org-3337	166	20	it	-PRON-	PRP
en-wikipedia-org-3337	166	21	is	be	VBZ
en-wikipedia-org-3337	166	22	unknown	unknown	JJ
en-wikipedia-org-3337	166	23	due	due	IN
en-wikipedia-org-3337	166	24	to	to	IN
en-wikipedia-org-3337	166	25	the	the	DT
en-wikipedia-org-3337	166	26	complexity	complexity	NN
en-wikipedia-org-3337	166	27	of	of	IN
en-wikipedia-org-3337	166	28	the	the	DT
en-wikipedia-org-3337	166	29	game	game	NN
en-wikipedia-org-3337	166	30	,	,	,
en-wikipedia-org-3337	166	31	for	for	IN
en-wikipedia-org-3337	166	32	instance	instance	NN
en-wikipedia-org-3337	166	33	in	in	IN
en-wikipedia-org-3337	166	34	Chinese	chinese	JJ
en-wikipedia-org-3337	166	35	chess	chess	NN
en-wikipedia-org-3337	166	36	.	.	.
en-wikipedia-org-3337	167	1	[	[	-LRB-
en-wikipedia-org-3337	167	2	20	20	CD
en-wikipedia-org-3337	167	3	]	]	-RRB-
en-wikipedia-org-3337	167	4	Or	or	CC
en-wikipedia-org-3337	167	5	,	,	,
en-wikipedia-org-3337	167	6	if	if	IN
en-wikipedia-org-3337	167	7	known	know	VBN
en-wikipedia-org-3337	167	8	,	,	,
en-wikipedia-org-3337	167	9	it	-PRON-	PRP
en-wikipedia-org-3337	167	10	may	may	MD
en-wikipedia-org-3337	167	11	not	not	RB
en-wikipedia-org-3337	167	12	be	be	VB
en-wikipedia-org-3337	167	13	known	know	VBN
en-wikipedia-org-3337	167	14	to	to	IN
en-wikipedia-org-3337	167	15	all	all	DT
en-wikipedia-org-3337	167	16	players	player	NNS
en-wikipedia-org-3337	167	17	,	,	,
en-wikipedia-org-3337	167	18	as	as	IN
en-wikipedia-org-3337	167	19	when	when	WRB
en-wikipedia-org-3337	167	20	playing	play	VBG
en-wikipedia-org-3337	167	21	tic	tic	JJ
en-wikipedia-org-3337	167	22	-	-	HYPH
en-wikipedia-org-3337	167	23	tac	tac	NN
en-wikipedia-org-3337	167	24	-	-	HYPH
en-wikipedia-org-3337	167	25	toe	toe	NN
en-wikipedia-org-3337	167	26	with	with	IN
en-wikipedia-org-3337	167	27	a	a	DT
en-wikipedia-org-3337	167	28	small	small	JJ
en-wikipedia-org-3337	167	29	child	child	NN
en-wikipedia-org-3337	167	30	who	who	WP
en-wikipedia-org-3337	167	31	desperately	desperately	RB
en-wikipedia-org-3337	167	32	wants	want	VBZ
en-wikipedia-org-3337	167	33	to	to	TO
en-wikipedia-org-3337	167	34	win	win	VB
en-wikipedia-org-3337	167	35	(	(	-LRB-
en-wikipedia-org-3337	167	36	meeting	meet	VBG
en-wikipedia-org-3337	167	37	the	the	DT
en-wikipedia-org-3337	167	38	other	other	JJ
en-wikipedia-org-3337	167	39	criteria	criterion	NNS
en-wikipedia-org-3337	167	40	)	)	-RRB-
en-wikipedia-org-3337	167	41	.	.	.
en-wikipedia-org-3337	168	1	The	the	DT
en-wikipedia-org-3337	168	2	criterion	criterion	NN
en-wikipedia-org-3337	168	3	of	of	IN
en-wikipedia-org-3337	168	4	common	common	JJ
en-wikipedia-org-3337	168	5	knowledge	knowledge	NN
en-wikipedia-org-3337	168	6	may	may	MD
en-wikipedia-org-3337	168	7	not	not	RB
en-wikipedia-org-3337	168	8	be	be	VB
en-wikipedia-org-3337	168	9	met	meet	VBN
en-wikipedia-org-3337	168	10	even	even	RB
en-wikipedia-org-3337	168	11	if	if	IN
en-wikipedia-org-3337	168	12	all	all	DT
en-wikipedia-org-3337	168	13	players	player	NNS
en-wikipedia-org-3337	168	14	do	do	VBP
en-wikipedia-org-3337	168	15	,	,	,
en-wikipedia-org-3337	168	16	in	in	IN
en-wikipedia-org-3337	168	17	fact	fact	NN
en-wikipedia-org-3337	168	18	,	,	,
en-wikipedia-org-3337	168	19	meet	meet	VB
en-wikipedia-org-3337	168	20	all	all	PDT
en-wikipedia-org-3337	168	21	the	the	DT
en-wikipedia-org-3337	168	22	other	other	JJ
en-wikipedia-org-3337	168	23	criteria	criterion	NNS
en-wikipedia-org-3337	168	24	.	.	.
en-wikipedia-org-3337	169	1	Players	player	NNS
en-wikipedia-org-3337	169	2	wrongly	wrongly	RB
en-wikipedia-org-3337	169	3	distrusting	distrust	VBG
en-wikipedia-org-3337	169	4	each	each	DT
en-wikipedia-org-3337	169	5	other	other	JJ
en-wikipedia-org-3337	169	6	's	's	POS
en-wikipedia-org-3337	169	7	rationality	rationality	NN
en-wikipedia-org-3337	169	8	may	may	MD
en-wikipedia-org-3337	169	9	adopt	adopt	VB
en-wikipedia-org-3337	169	10	counter	counter	NNS
en-wikipedia-org-3337	169	11	-	-	NNS
en-wikipedia-org-3337	169	12	strategies	strategy	NNS
en-wikipedia-org-3337	169	13	to	to	IN
en-wikipedia-org-3337	169	14	expected	expect	VBN
en-wikipedia-org-3337	169	15	irrational	irrational	JJ
en-wikipedia-org-3337	169	16	play	play	NN
en-wikipedia-org-3337	169	17	on	on	IN
en-wikipedia-org-3337	169	18	their	-PRON-	PRP$
en-wikipedia-org-3337	169	19	opponents	opponent	NNS
en-wikipedia-org-3337	169	20	’	’	POS
en-wikipedia-org-3337	169	21	behalf	behalf	NN
en-wikipedia-org-3337	169	22	.	.	.
en-wikipedia-org-3337	170	1	This	this	DT
en-wikipedia-org-3337	170	2	is	be	VBZ
en-wikipedia-org-3337	170	3	a	a	DT
en-wikipedia-org-3337	170	4	major	major	JJ
en-wikipedia-org-3337	170	5	consideration	consideration	NN
en-wikipedia-org-3337	170	6	in	in	IN
en-wikipedia-org-3337	170	7	"	"	``
en-wikipedia-org-3337	170	8	chicken	chicken	NN
en-wikipedia-org-3337	170	9	"	"	''
en-wikipedia-org-3337	170	10	or	or	CC
en-wikipedia-org-3337	170	11	an	an	DT
en-wikipedia-org-3337	170	12	arms	arm	NNS
en-wikipedia-org-3337	170	13	race	race	NN
en-wikipedia-org-3337	170	14	,	,	,
en-wikipedia-org-3337	170	15	for	for	IN
en-wikipedia-org-3337	170	16	example	example	NN
en-wikipedia-org-3337	170	17	.	.	.
en-wikipedia-org-3337	171	1	Where	where	WRB
en-wikipedia-org-3337	171	2	the	the	DT
en-wikipedia-org-3337	171	3	conditions	condition	NNS
en-wikipedia-org-3337	171	4	are	be	VBP
en-wikipedia-org-3337	171	5	met[edit	met[edit	NN
en-wikipedia-org-3337	171	6	]	]	-RRB-
en-wikipedia-org-3337	171	7	In	in	IN
en-wikipedia-org-3337	171	8	his	-PRON-	PRP$
en-wikipedia-org-3337	171	9	Ph.D.	ph.d.	NN
en-wikipedia-org-3337	171	10	dissertation	dissertation	NN
en-wikipedia-org-3337	171	11	,	,	,
en-wikipedia-org-3337	171	12	John	John	NNP
en-wikipedia-org-3337	171	13	Nash	Nash	NNP
en-wikipedia-org-3337	171	14	proposed	propose	VBD
en-wikipedia-org-3337	171	15	two	two	CD
en-wikipedia-org-3337	171	16	interpretations	interpretation	NNS
en-wikipedia-org-3337	171	17	of	of	IN
en-wikipedia-org-3337	171	18	his	-PRON-	PRP$
en-wikipedia-org-3337	171	19	equilibrium	equilibrium	NN
en-wikipedia-org-3337	171	20	concept	concept	NN
en-wikipedia-org-3337	171	21	,	,	,
en-wikipedia-org-3337	171	22	with	with	IN
en-wikipedia-org-3337	171	23	the	the	DT
en-wikipedia-org-3337	171	24	objective	objective	NN
en-wikipedia-org-3337	171	25	of	of	IN
en-wikipedia-org-3337	171	26	showing	show	VBG
en-wikipedia-org-3337	171	27	how	how	WRB
en-wikipedia-org-3337	171	28	equilibrium	equilibrium	NN
en-wikipedia-org-3337	171	29	points	point	NNS
en-wikipedia-org-3337	171	30	can	can	MD
en-wikipedia-org-3337	171	31	be	be	VB
en-wikipedia-org-3337	171	32	connected	connect	VBN
en-wikipedia-org-3337	171	33	with	with	IN
en-wikipedia-org-3337	171	34	observable	observable	JJ
en-wikipedia-org-3337	171	35	phenomenon	phenomenon	NN
en-wikipedia-org-3337	171	36	.	.	.
en-wikipedia-org-3337	172	1	(	(	-LRB-
en-wikipedia-org-3337	172	2	...	...	NFP
en-wikipedia-org-3337	172	3	)	)	-RRB-
en-wikipedia-org-3337	172	4	One	one	CD
en-wikipedia-org-3337	172	5	interpretation	interpretation	NN
en-wikipedia-org-3337	172	6	is	be	VBZ
en-wikipedia-org-3337	172	7	rationalistic	rationalistic	JJ
en-wikipedia-org-3337	172	8	:	:	:
en-wikipedia-org-3337	172	9	if	if	IN
en-wikipedia-org-3337	172	10	we	-PRON-	PRP
en-wikipedia-org-3337	172	11	assume	assume	VBP
en-wikipedia-org-3337	172	12	that	that	IN
en-wikipedia-org-3337	172	13	players	player	NNS
en-wikipedia-org-3337	172	14	are	be	VBP
en-wikipedia-org-3337	172	15	rational	rational	JJ
en-wikipedia-org-3337	172	16	,	,	,
en-wikipedia-org-3337	172	17	know	know	VBP
en-wikipedia-org-3337	172	18	the	the	DT
en-wikipedia-org-3337	172	19	full	full	JJ
en-wikipedia-org-3337	172	20	structure	structure	NN
en-wikipedia-org-3337	172	21	of	of	IN
en-wikipedia-org-3337	172	22	the	the	DT
en-wikipedia-org-3337	172	23	game	game	NN
en-wikipedia-org-3337	172	24	,	,	,
en-wikipedia-org-3337	172	25	the	the	DT
en-wikipedia-org-3337	172	26	game	game	NN
en-wikipedia-org-3337	172	27	is	be	VBZ
en-wikipedia-org-3337	172	28	played	play	VBN
en-wikipedia-org-3337	172	29	just	just	RB
en-wikipedia-org-3337	172	30	once	once	RB
en-wikipedia-org-3337	172	31	,	,	,
en-wikipedia-org-3337	172	32	and	and	CC
en-wikipedia-org-3337	172	33	there	there	EX
en-wikipedia-org-3337	172	34	is	be	VBZ
en-wikipedia-org-3337	172	35	just	just	RB
en-wikipedia-org-3337	172	36	one	one	CD
en-wikipedia-org-3337	172	37	Nash	Nash	NNP
en-wikipedia-org-3337	172	38	equilibrium	equilibrium	NN
en-wikipedia-org-3337	172	39	,	,	,
en-wikipedia-org-3337	172	40	then	then	RB
en-wikipedia-org-3337	172	41	players	player	NNS
en-wikipedia-org-3337	172	42	will	will	MD
en-wikipedia-org-3337	172	43	play	play	VB
en-wikipedia-org-3337	172	44	according	accord	VBG
en-wikipedia-org-3337	172	45	to	to	IN
en-wikipedia-org-3337	172	46	that	that	DT
en-wikipedia-org-3337	172	47	equilibrium	equilibrium	NN
en-wikipedia-org-3337	172	48	.	.	.
en-wikipedia-org-3337	173	1	This	this	DT
en-wikipedia-org-3337	173	2	idea	idea	NN
en-wikipedia-org-3337	173	3	was	be	VBD
en-wikipedia-org-3337	173	4	formalized	formalize	VBN
en-wikipedia-org-3337	173	5	by	by	IN
en-wikipedia-org-3337	173	6	Aumann	Aumann	NNP
en-wikipedia-org-3337	173	7	,	,	,
en-wikipedia-org-3337	173	8	R.	R.	NNP
en-wikipedia-org-3337	173	9	and	and	CC
en-wikipedia-org-3337	173	10	A.	A.	NNP
en-wikipedia-org-3337	173	11	Brandenburger	Brandenburger	NNP
en-wikipedia-org-3337	173	12	,	,	,
en-wikipedia-org-3337	173	13	1995	1995	CD
en-wikipedia-org-3337	173	14	,	,	,
en-wikipedia-org-3337	173	15	Epistemic	Epistemic	NNP
en-wikipedia-org-3337	173	16	Conditions	Conditions	NNPS
en-wikipedia-org-3337	173	17	for	for	IN
en-wikipedia-org-3337	173	18	Nash	Nash	NNP
en-wikipedia-org-3337	173	19	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	173	20	,	,	,
en-wikipedia-org-3337	173	21	Econometrica	Econometrica	NNP
en-wikipedia-org-3337	173	22	,	,	,
en-wikipedia-org-3337	173	23	63	63	CD
en-wikipedia-org-3337	173	24	,	,	,
en-wikipedia-org-3337	173	25	1161	1161	CD
en-wikipedia-org-3337	173	26	-	-	SYM
en-wikipedia-org-3337	173	27	1180	1180	CD
en-wikipedia-org-3337	173	28	who	who	WP
en-wikipedia-org-3337	173	29	interpreted	interpret	VBD
en-wikipedia-org-3337	173	30	each	each	DT
en-wikipedia-org-3337	173	31	player	player	NN
en-wikipedia-org-3337	173	32	's	's	POS
en-wikipedia-org-3337	173	33	mixed	mixed	JJ
en-wikipedia-org-3337	173	34	strategy	strategy	NN
en-wikipedia-org-3337	173	35	as	as	IN
en-wikipedia-org-3337	173	36	a	a	DT
en-wikipedia-org-3337	173	37	conjecture	conjecture	NN
en-wikipedia-org-3337	173	38	about	about	IN
en-wikipedia-org-3337	173	39	the	the	DT
en-wikipedia-org-3337	173	40	behaviour	behaviour	NN
en-wikipedia-org-3337	173	41	of	of	IN
en-wikipedia-org-3337	173	42	other	other	JJ
en-wikipedia-org-3337	173	43	players	player	NNS
en-wikipedia-org-3337	173	44	and	and	CC
en-wikipedia-org-3337	173	45	have	have	VBP
en-wikipedia-org-3337	173	46	shown	show	VBN
en-wikipedia-org-3337	173	47	that	that	IN
en-wikipedia-org-3337	173	48	if	if	IN
en-wikipedia-org-3337	173	49	the	the	DT
en-wikipedia-org-3337	173	50	game	game	NN
en-wikipedia-org-3337	173	51	and	and	CC
en-wikipedia-org-3337	173	52	the	the	DT
en-wikipedia-org-3337	173	53	rationality	rationality	NN
en-wikipedia-org-3337	173	54	of	of	IN
en-wikipedia-org-3337	173	55	players	player	NNS
en-wikipedia-org-3337	173	56	is	be	VBZ
en-wikipedia-org-3337	173	57	mutually	mutually	RB
en-wikipedia-org-3337	173	58	known	know	VBN
en-wikipedia-org-3337	173	59	and	and	CC
en-wikipedia-org-3337	173	60	these	these	DT
en-wikipedia-org-3337	173	61	conjectures	conjecture	NNS
en-wikipedia-org-3337	173	62	are	be	VBP
en-wikipedia-org-3337	173	63	commonly	commonly	RB
en-wikipedia-org-3337	173	64	know	know	VBP
en-wikipedia-org-3337	173	65	,	,	,
en-wikipedia-org-3337	173	66	then	then	RB
en-wikipedia-org-3337	173	67	the	the	DT
en-wikipedia-org-3337	173	68	conjectures	conjecture	NNS
en-wikipedia-org-3337	173	69	must	must	MD
en-wikipedia-org-3337	173	70	be	be	VB
en-wikipedia-org-3337	173	71	a	a	DT
en-wikipedia-org-3337	173	72	Nash	Nash	NNP
en-wikipedia-org-3337	173	73	equilibrium	equilibrium	NN
en-wikipedia-org-3337	173	74	(	(	-LRB-
en-wikipedia-org-3337	173	75	a	a	DT
en-wikipedia-org-3337	173	76	common	common	JJ
en-wikipedia-org-3337	173	77	prior	prior	JJ
en-wikipedia-org-3337	173	78	assumption	assumption	NN
en-wikipedia-org-3337	173	79	is	be	VBZ
en-wikipedia-org-3337	173	80	needed	need	VBN
en-wikipedia-org-3337	173	81	for	for	IN
en-wikipedia-org-3337	173	82	this	this	DT
en-wikipedia-org-3337	173	83	result	result	NN
en-wikipedia-org-3337	173	84	in	in	IN
en-wikipedia-org-3337	173	85	general	general	JJ
en-wikipedia-org-3337	173	86	,	,	,
en-wikipedia-org-3337	173	87	but	but	CC
en-wikipedia-org-3337	173	88	not	not	RB
en-wikipedia-org-3337	173	89	in	in	IN
en-wikipedia-org-3337	173	90	the	the	DT
en-wikipedia-org-3337	173	91	case	case	NN
en-wikipedia-org-3337	173	92	of	of	IN
en-wikipedia-org-3337	173	93	two	two	CD
en-wikipedia-org-3337	173	94	players	player	NNS
en-wikipedia-org-3337	173	95	.	.	.
en-wikipedia-org-3337	174	1	In	in	IN
en-wikipedia-org-3337	174	2	this	this	DT
en-wikipedia-org-3337	174	3	case	case	NN
en-wikipedia-org-3337	174	4	,	,	,
en-wikipedia-org-3337	174	5	the	the	DT
en-wikipedia-org-3337	174	6	conjectures	conjecture	NNS
en-wikipedia-org-3337	174	7	need	nee	MD
en-wikipedia-org-3337	174	8	only	only	RB
en-wikipedia-org-3337	174	9	be	be	VB
en-wikipedia-org-3337	174	10	mutually	mutually	RB
en-wikipedia-org-3337	174	11	known	know	VBN
en-wikipedia-org-3337	174	12	)	)	-RRB-
en-wikipedia-org-3337	174	13	.	.	.
en-wikipedia-org-3337	175	1	A	a	DT
en-wikipedia-org-3337	175	2	second	second	JJ
en-wikipedia-org-3337	175	3	interpretation	interpretation	NN
en-wikipedia-org-3337	175	4	,	,	,
en-wikipedia-org-3337	175	5	that	that	IN
en-wikipedia-org-3337	175	6	Nash	Nash	NNP
en-wikipedia-org-3337	175	7	referred	refer	VBD
en-wikipedia-org-3337	175	8	to	to	IN
en-wikipedia-org-3337	175	9	by	by	IN
en-wikipedia-org-3337	175	10	the	the	DT
en-wikipedia-org-3337	175	11	mass	mass	NN
en-wikipedia-org-3337	175	12	action	action	NN
en-wikipedia-org-3337	175	13	interpretation	interpretation	NN
en-wikipedia-org-3337	175	14	,	,	,
en-wikipedia-org-3337	175	15	is	be	VBZ
en-wikipedia-org-3337	175	16	less	less	RBR
en-wikipedia-org-3337	175	17	demanding	demand	VBG
en-wikipedia-org-3337	175	18	on	on	IN
en-wikipedia-org-3337	175	19	players	player	NNS
en-wikipedia-org-3337	175	20	:	:	:
en-wikipedia-org-3337	175	21	[	[	-LRB-
en-wikipedia-org-3337	175	22	i]t	i]t	NN
en-wikipedia-org-3337	175	23	is	be	VBZ
en-wikipedia-org-3337	175	24	unnecessary	unnecessary	JJ
en-wikipedia-org-3337	175	25	to	to	TO
en-wikipedia-org-3337	175	26	assume	assume	VB
en-wikipedia-org-3337	175	27	that	that	IN
en-wikipedia-org-3337	175	28	the	the	DT
en-wikipedia-org-3337	175	29	participants	participant	NNS
en-wikipedia-org-3337	175	30	have	have	VBP
en-wikipedia-org-3337	175	31	full	full	JJ
en-wikipedia-org-3337	175	32	knowledge	knowledge	NN
en-wikipedia-org-3337	175	33	of	of	IN
en-wikipedia-org-3337	175	34	the	the	DT
en-wikipedia-org-3337	175	35	total	total	JJ
en-wikipedia-org-3337	175	36	structure	structure	NN
en-wikipedia-org-3337	175	37	of	of	IN
en-wikipedia-org-3337	175	38	the	the	DT
en-wikipedia-org-3337	175	39	game	game	NN
en-wikipedia-org-3337	175	40	,	,	,
en-wikipedia-org-3337	175	41	or	or	CC
en-wikipedia-org-3337	175	42	the	the	DT
en-wikipedia-org-3337	175	43	ability	ability	NN
en-wikipedia-org-3337	175	44	and	and	CC
en-wikipedia-org-3337	175	45	inclination	inclination	NN
en-wikipedia-org-3337	175	46	to	to	TO
en-wikipedia-org-3337	175	47	go	go	VB
en-wikipedia-org-3337	175	48	through	through	IN
en-wikipedia-org-3337	175	49	any	any	DT
en-wikipedia-org-3337	175	50	complex	complex	JJ
en-wikipedia-org-3337	175	51	reasoning	reasoning	NN
en-wikipedia-org-3337	175	52	processes	process	NNS
en-wikipedia-org-3337	175	53	.	.	.
en-wikipedia-org-3337	176	1	What	what	WP
en-wikipedia-org-3337	176	2	is	be	VBZ
en-wikipedia-org-3337	176	3	assumed	assume	VBN
en-wikipedia-org-3337	176	4	is	be	VBZ
en-wikipedia-org-3337	176	5	that	that	IN
en-wikipedia-org-3337	176	6	there	there	EX
en-wikipedia-org-3337	176	7	is	be	VBZ
en-wikipedia-org-3337	176	8	a	a	DT
en-wikipedia-org-3337	176	9	population	population	NN
en-wikipedia-org-3337	176	10	of	of	IN
en-wikipedia-org-3337	176	11	participants	participant	NNS
en-wikipedia-org-3337	176	12	for	for	IN
en-wikipedia-org-3337	176	13	each	each	DT
en-wikipedia-org-3337	176	14	position	position	NN
en-wikipedia-org-3337	176	15	in	in	IN
en-wikipedia-org-3337	176	16	the	the	DT
en-wikipedia-org-3337	176	17	game	game	NN
en-wikipedia-org-3337	176	18	,	,	,
en-wikipedia-org-3337	176	19	which	which	WDT
en-wikipedia-org-3337	176	20	will	will	MD
en-wikipedia-org-3337	176	21	be	be	VB
en-wikipedia-org-3337	176	22	played	play	VBN
en-wikipedia-org-3337	176	23	throughout	throughout	IN
en-wikipedia-org-3337	176	24	time	time	NN
en-wikipedia-org-3337	176	25	by	by	IN
en-wikipedia-org-3337	176	26	participants	participant	NNS
en-wikipedia-org-3337	176	27	drawn	draw	VBN
en-wikipedia-org-3337	176	28	at	at	IN
en-wikipedia-org-3337	176	29	random	random	JJ
en-wikipedia-org-3337	176	30	from	from	IN
en-wikipedia-org-3337	176	31	the	the	DT
en-wikipedia-org-3337	176	32	different	different	JJ
en-wikipedia-org-3337	176	33	populations	population	NNS
en-wikipedia-org-3337	176	34	.	.	.
en-wikipedia-org-3337	177	1	If	if	IN
en-wikipedia-org-3337	177	2	there	there	EX
en-wikipedia-org-3337	177	3	is	be	VBZ
en-wikipedia-org-3337	177	4	a	a	DT
en-wikipedia-org-3337	177	5	stable	stable	JJ
en-wikipedia-org-3337	177	6	average	average	JJ
en-wikipedia-org-3337	177	7	frequency	frequency	NN
en-wikipedia-org-3337	177	8	with	with	IN
en-wikipedia-org-3337	177	9	which	which	WDT
en-wikipedia-org-3337	177	10	each	each	DT
en-wikipedia-org-3337	177	11	pure	pure	JJ
en-wikipedia-org-3337	177	12	strategy	strategy	NN
en-wikipedia-org-3337	177	13	is	be	VBZ
en-wikipedia-org-3337	177	14	employed	employ	VBN
en-wikipedia-org-3337	177	15	by	by	IN
en-wikipedia-org-3337	177	16	the	the	DT
en-wikipedia-org-3337	177	17	average	average	JJ
en-wikipedia-org-3337	177	18	member	member	NN
en-wikipedia-org-3337	177	19	of	of	IN
en-wikipedia-org-3337	177	20	the	the	DT
en-wikipedia-org-3337	177	21	appropriate	appropriate	JJ
en-wikipedia-org-3337	177	22	population	population	NN
en-wikipedia-org-3337	177	23	,	,	,
en-wikipedia-org-3337	177	24	then	then	RB
en-wikipedia-org-3337	177	25	this	this	DT
en-wikipedia-org-3337	177	26	stable	stable	JJ
en-wikipedia-org-3337	177	27	average	average	JJ
en-wikipedia-org-3337	177	28	frequency	frequency	NN
en-wikipedia-org-3337	177	29	constitutes	constitute	VBZ
en-wikipedia-org-3337	177	30	a	a	DT
en-wikipedia-org-3337	177	31	mixed	mixed	JJ
en-wikipedia-org-3337	177	32	strategy	strategy	NN
en-wikipedia-org-3337	177	33	Nash	Nash	NNP
en-wikipedia-org-3337	177	34	equilibrium	equilibrium	NN
en-wikipedia-org-3337	177	35	.	.	.
en-wikipedia-org-3337	178	1	For	for	IN
en-wikipedia-org-3337	178	2	a	a	DT
en-wikipedia-org-3337	178	3	formal	formal	JJ
en-wikipedia-org-3337	178	4	result	result	NN
en-wikipedia-org-3337	178	5	along	along	IN
en-wikipedia-org-3337	178	6	these	these	DT
en-wikipedia-org-3337	178	7	lines	line	NNS
en-wikipedia-org-3337	178	8	,	,	,
en-wikipedia-org-3337	178	9	see	see	VB
en-wikipedia-org-3337	178	10	Kuhn	Kuhn	NNP
en-wikipedia-org-3337	178	11	,	,	,
en-wikipedia-org-3337	178	12	H.	H.	NNP
en-wikipedia-org-3337	178	13	and	and	CC
en-wikipedia-org-3337	178	14	et	et	NNP
en-wikipedia-org-3337	178	15	al	al	NNP
en-wikipedia-org-3337	178	16	.	.	NNP
en-wikipedia-org-3337	178	17	,	,	,
en-wikipedia-org-3337	178	18	1996	1996	CD
en-wikipedia-org-3337	178	19	,	,	,
en-wikipedia-org-3337	178	20	"	"	``
en-wikipedia-org-3337	178	21	The	the	DT
en-wikipedia-org-3337	178	22	Work	work	NN
en-wikipedia-org-3337	178	23	of	of	IN
en-wikipedia-org-3337	178	24	John	John	NNP
en-wikipedia-org-3337	178	25	Nash	Nash	NNP
en-wikipedia-org-3337	178	26	in	in	IN
en-wikipedia-org-3337	178	27	Game	Game	NNP
en-wikipedia-org-3337	178	28	Theory	Theory	NNP
en-wikipedia-org-3337	178	29	,	,	,
en-wikipedia-org-3337	178	30	"	"	''
en-wikipedia-org-3337	178	31	Journal	Journal	NNP
en-wikipedia-org-3337	178	32	of	of	IN
en-wikipedia-org-3337	178	33	Economic	Economic	NNP
en-wikipedia-org-3337	178	34	Theory	Theory	NNP
en-wikipedia-org-3337	178	35	,	,	,
en-wikipedia-org-3337	178	36	69	69	CD
en-wikipedia-org-3337	178	37	,	,	,
en-wikipedia-org-3337	178	38	153–185	153–185	CD
en-wikipedia-org-3337	178	39	.	.	.
en-wikipedia-org-3337	179	1	Due	due	IN
en-wikipedia-org-3337	179	2	to	to	IN
en-wikipedia-org-3337	179	3	the	the	DT
en-wikipedia-org-3337	179	4	limited	limit	VBN
en-wikipedia-org-3337	179	5	conditions	condition	NNS
en-wikipedia-org-3337	179	6	in	in	IN
en-wikipedia-org-3337	179	7	which	which	WDT
en-wikipedia-org-3337	179	8	NE	NE	NNP
en-wikipedia-org-3337	179	9	can	can	MD
en-wikipedia-org-3337	179	10	actually	actually	RB
en-wikipedia-org-3337	179	11	be	be	VB
en-wikipedia-org-3337	179	12	observed	observe	VBN
en-wikipedia-org-3337	179	13	,	,	,
en-wikipedia-org-3337	179	14	they	-PRON-	PRP
en-wikipedia-org-3337	179	15	are	be	VBP
en-wikipedia-org-3337	179	16	rarely	rarely	RB
en-wikipedia-org-3337	179	17	treated	treat	VBN
en-wikipedia-org-3337	179	18	as	as	IN
en-wikipedia-org-3337	179	19	a	a	DT
en-wikipedia-org-3337	179	20	guide	guide	NN
en-wikipedia-org-3337	179	21	to	to	IN
en-wikipedia-org-3337	179	22	day	day	NN
en-wikipedia-org-3337	179	23	-	-	HYPH
en-wikipedia-org-3337	179	24	to	to	IN
en-wikipedia-org-3337	179	25	-	-	HYPH
en-wikipedia-org-3337	179	26	day	day	NN
en-wikipedia-org-3337	179	27	behaviour	behaviour	NN
en-wikipedia-org-3337	179	28	,	,	,
en-wikipedia-org-3337	179	29	or	or	CC
en-wikipedia-org-3337	179	30	observed	observe	VBN
en-wikipedia-org-3337	179	31	in	in	IN
en-wikipedia-org-3337	179	32	practice	practice	NN
en-wikipedia-org-3337	179	33	in	in	IN
en-wikipedia-org-3337	179	34	human	human	JJ
en-wikipedia-org-3337	179	35	negotiations	negotiation	NNS
en-wikipedia-org-3337	179	36	.	.	.
en-wikipedia-org-3337	180	1	However	however	RB
en-wikipedia-org-3337	180	2	,	,	,
en-wikipedia-org-3337	180	3	as	as	IN
en-wikipedia-org-3337	180	4	a	a	DT
en-wikipedia-org-3337	180	5	theoretical	theoretical	JJ
en-wikipedia-org-3337	180	6	concept	concept	NN
en-wikipedia-org-3337	180	7	in	in	IN
en-wikipedia-org-3337	180	8	economics	economic	NNS
en-wikipedia-org-3337	180	9	and	and	CC
en-wikipedia-org-3337	180	10	evolutionary	evolutionary	JJ
en-wikipedia-org-3337	180	11	biology	biology	NN
en-wikipedia-org-3337	180	12	,	,	,
en-wikipedia-org-3337	180	13	the	the	DT
en-wikipedia-org-3337	180	14	NE	NE	NNP
en-wikipedia-org-3337	180	15	has	have	VBZ
en-wikipedia-org-3337	180	16	explanatory	explanatory	JJ
en-wikipedia-org-3337	180	17	power	power	NN
en-wikipedia-org-3337	180	18	.	.	.
en-wikipedia-org-3337	181	1	The	the	DT
en-wikipedia-org-3337	181	2	payoff	payoff	NN
en-wikipedia-org-3337	181	3	in	in	IN
en-wikipedia-org-3337	181	4	economics	economics	NN
en-wikipedia-org-3337	181	5	is	be	VBZ
en-wikipedia-org-3337	181	6	utility	utility	NN
en-wikipedia-org-3337	181	7	(	(	-LRB-
en-wikipedia-org-3337	181	8	or	or	CC
en-wikipedia-org-3337	181	9	sometimes	sometimes	RB
en-wikipedia-org-3337	181	10	money	money	NN
en-wikipedia-org-3337	181	11	)	)	-RRB-
en-wikipedia-org-3337	181	12	,	,	,
en-wikipedia-org-3337	181	13	and	and	CC
en-wikipedia-org-3337	181	14	in	in	IN
en-wikipedia-org-3337	181	15	evolutionary	evolutionary	JJ
en-wikipedia-org-3337	181	16	biology	biology	NN
en-wikipedia-org-3337	181	17	is	be	VBZ
en-wikipedia-org-3337	181	18	gene	gene	NN
en-wikipedia-org-3337	181	19	transmission	transmission	NN
en-wikipedia-org-3337	181	20	;	;	:
en-wikipedia-org-3337	181	21	both	both	DT
en-wikipedia-org-3337	181	22	are	be	VBP
en-wikipedia-org-3337	181	23	the	the	DT
en-wikipedia-org-3337	181	24	fundamental	fundamental	JJ
en-wikipedia-org-3337	181	25	bottom	bottom	JJ
en-wikipedia-org-3337	181	26	line	line	NN
en-wikipedia-org-3337	181	27	of	of	IN
en-wikipedia-org-3337	181	28	survival	survival	NN
en-wikipedia-org-3337	181	29	.	.	.
en-wikipedia-org-3337	182	1	Researchers	researcher	NNS
en-wikipedia-org-3337	182	2	who	who	WP
en-wikipedia-org-3337	182	3	apply	apply	VBP
en-wikipedia-org-3337	182	4	games	game	NNS
en-wikipedia-org-3337	182	5	theory	theory	NN
en-wikipedia-org-3337	182	6	in	in	IN
en-wikipedia-org-3337	182	7	these	these	DT
en-wikipedia-org-3337	182	8	fields	field	NNS
en-wikipedia-org-3337	182	9	claim	claim	VBP
en-wikipedia-org-3337	182	10	that	that	IN
en-wikipedia-org-3337	182	11	strategies	strategy	NNS
en-wikipedia-org-3337	182	12	failing	fail	VBG
en-wikipedia-org-3337	182	13	to	to	TO
en-wikipedia-org-3337	182	14	maximize	maximize	VB
en-wikipedia-org-3337	182	15	these	these	DT
en-wikipedia-org-3337	182	16	for	for	IN
en-wikipedia-org-3337	182	17	whatever	whatever	WDT
en-wikipedia-org-3337	182	18	reason	reason	NN
en-wikipedia-org-3337	182	19	will	will	MD
en-wikipedia-org-3337	182	20	be	be	VB
en-wikipedia-org-3337	182	21	competed	compete	VBN
en-wikipedia-org-3337	182	22	out	out	IN
en-wikipedia-org-3337	182	23	of	of	IN
en-wikipedia-org-3337	182	24	the	the	DT
en-wikipedia-org-3337	182	25	market	market	NN
en-wikipedia-org-3337	182	26	or	or	CC
en-wikipedia-org-3337	182	27	environment	environment	NN
en-wikipedia-org-3337	182	28	,	,	,
en-wikipedia-org-3337	182	29	which	which	WDT
en-wikipedia-org-3337	182	30	are	be	VBP
en-wikipedia-org-3337	182	31	ascribed	ascribe	VBN
en-wikipedia-org-3337	182	32	the	the	DT
en-wikipedia-org-3337	182	33	ability	ability	NN
en-wikipedia-org-3337	182	34	to	to	TO
en-wikipedia-org-3337	182	35	test	test	VB
en-wikipedia-org-3337	182	36	all	all	DT
en-wikipedia-org-3337	182	37	strategies	strategy	NNS
en-wikipedia-org-3337	182	38	.	.	.
en-wikipedia-org-3337	183	1	This	this	DT
en-wikipedia-org-3337	183	2	conclusion	conclusion	NN
en-wikipedia-org-3337	183	3	is	be	VBZ
en-wikipedia-org-3337	183	4	drawn	draw	VBN
en-wikipedia-org-3337	183	5	from	from	IN
en-wikipedia-org-3337	183	6	the	the	DT
en-wikipedia-org-3337	183	7	"	"	``
en-wikipedia-org-3337	183	8	stability	stability	NN
en-wikipedia-org-3337	183	9	"	"	''
en-wikipedia-org-3337	183	10	theory	theory	NN
en-wikipedia-org-3337	183	11	above	above	RB
en-wikipedia-org-3337	183	12	.	.	.
en-wikipedia-org-3337	184	1	In	in	IN
en-wikipedia-org-3337	184	2	these	these	DT
en-wikipedia-org-3337	184	3	situations	situation	NNS
en-wikipedia-org-3337	184	4	the	the	DT
en-wikipedia-org-3337	184	5	assumption	assumption	NN
en-wikipedia-org-3337	184	6	that	that	IN
en-wikipedia-org-3337	184	7	the	the	DT
en-wikipedia-org-3337	184	8	strategy	strategy	NN
en-wikipedia-org-3337	184	9	observed	observe	VBN
en-wikipedia-org-3337	184	10	is	be	VBZ
en-wikipedia-org-3337	184	11	actually	actually	RB
en-wikipedia-org-3337	184	12	a	a	DT
en-wikipedia-org-3337	184	13	NE	NE	NNP
en-wikipedia-org-3337	184	14	has	have	VBZ
en-wikipedia-org-3337	184	15	often	often	RB
en-wikipedia-org-3337	184	16	been	be	VBN
en-wikipedia-org-3337	184	17	borne	bear	VBN
en-wikipedia-org-3337	184	18	out	out	RP
en-wikipedia-org-3337	184	19	by	by	IN
en-wikipedia-org-3337	184	20	research	research	NN
en-wikipedia-org-3337	184	21	.	.	.
en-wikipedia-org-3337	185	1	[	[	-LRB-
en-wikipedia-org-3337	185	2	21	21	CD
en-wikipedia-org-3337	185	3	]	]	-RRB-
en-wikipedia-org-3337	185	4	NE	NE	NNP
en-wikipedia-org-3337	185	5	and	and	CC
en-wikipedia-org-3337	185	6	non	non	JJ
en-wikipedia-org-3337	185	7	-	-	JJ
en-wikipedia-org-3337	185	8	credible	credible	JJ
en-wikipedia-org-3337	185	9	threats[edit	threats[edit	NFP
en-wikipedia-org-3337	185	10	]	]	-RRB-
en-wikipedia-org-3337	185	11	Extensive	extensive	JJ
en-wikipedia-org-3337	185	12	and	and	CC
en-wikipedia-org-3337	185	13	Normal	normal	JJ
en-wikipedia-org-3337	185	14	form	form	NN
en-wikipedia-org-3337	185	15	illustrations	illustration	NNS
en-wikipedia-org-3337	185	16	that	that	WDT
en-wikipedia-org-3337	185	17	show	show	VBP
en-wikipedia-org-3337	185	18	the	the	DT
en-wikipedia-org-3337	185	19	difference	difference	NN
en-wikipedia-org-3337	185	20	between	between	IN
en-wikipedia-org-3337	185	21	SPNE	SPNE	NNP
en-wikipedia-org-3337	185	22	and	and	CC
en-wikipedia-org-3337	185	23	other	other	JJ
en-wikipedia-org-3337	185	24	NE	NE	NNP
en-wikipedia-org-3337	185	25	.	.	.
en-wikipedia-org-3337	186	1	The	the	DT
en-wikipedia-org-3337	186	2	blue	blue	JJ
en-wikipedia-org-3337	186	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	186	4	is	be	VBZ
en-wikipedia-org-3337	186	5	not	not	RB
en-wikipedia-org-3337	186	6	subgame	subgame	VBN
en-wikipedia-org-3337	186	7	perfect	perfect	JJ
en-wikipedia-org-3337	186	8	because	because	IN
en-wikipedia-org-3337	186	9	player	player	NN
en-wikipedia-org-3337	186	10	two	two	CD
en-wikipedia-org-3337	186	11	makes	make	VBZ
en-wikipedia-org-3337	186	12	a	a	DT
en-wikipedia-org-3337	186	13	non	non	JJ
en-wikipedia-org-3337	186	14	-	-	JJ
en-wikipedia-org-3337	186	15	credible	credible	JJ
en-wikipedia-org-3337	186	16	threat	threat	NN
en-wikipedia-org-3337	186	17	at	at	IN
en-wikipedia-org-3337	186	18	2(2	2(2	NNP
en-wikipedia-org-3337	186	19	)	)	-RRB-
en-wikipedia-org-3337	186	20	to	to	TO
en-wikipedia-org-3337	186	21	be	be	VB
en-wikipedia-org-3337	186	22	unkind	unkind	JJ
en-wikipedia-org-3337	186	23	(	(	-LRB-
en-wikipedia-org-3337	186	24	U	u	NN
en-wikipedia-org-3337	186	25	)	)	-RRB-
en-wikipedia-org-3337	186	26	.	.	.
en-wikipedia-org-3337	187	1	The	the	DT
en-wikipedia-org-3337	187	2	Nash	Nash	NNP
en-wikipedia-org-3337	187	3	equilibrium	equilibrium	NN
en-wikipedia-org-3337	187	4	is	be	VBZ
en-wikipedia-org-3337	187	5	a	a	DT
en-wikipedia-org-3337	187	6	superset	superset	NN
en-wikipedia-org-3337	187	7	of	of	IN
en-wikipedia-org-3337	187	8	the	the	DT
en-wikipedia-org-3337	187	9	subgame	subgame	NN
en-wikipedia-org-3337	187	10	perfect	perfect	JJ
en-wikipedia-org-3337	187	11	Nash	Nash	NNP
en-wikipedia-org-3337	187	12	equilibrium	equilibrium	NN
en-wikipedia-org-3337	187	13	.	.	.
en-wikipedia-org-3337	188	1	The	the	DT
en-wikipedia-org-3337	188	2	subgame	subgame	NN
en-wikipedia-org-3337	188	3	perfect	perfect	JJ
en-wikipedia-org-3337	188	4	equilibrium	equilibrium	NN
en-wikipedia-org-3337	188	5	in	in	IN
en-wikipedia-org-3337	188	6	addition	addition	NN
en-wikipedia-org-3337	188	7	to	to	IN
en-wikipedia-org-3337	188	8	the	the	DT
en-wikipedia-org-3337	188	9	Nash	Nash	NNP
en-wikipedia-org-3337	188	10	equilibrium	equilibrium	NN
en-wikipedia-org-3337	188	11	requires	require	VBZ
en-wikipedia-org-3337	188	12	that	that	IN
en-wikipedia-org-3337	188	13	the	the	DT
en-wikipedia-org-3337	188	14	strategy	strategy	NN
en-wikipedia-org-3337	188	15	also	also	RB
en-wikipedia-org-3337	188	16	is	be	VBZ
en-wikipedia-org-3337	188	17	a	a	DT
en-wikipedia-org-3337	188	18	Nash	Nash	NNP
en-wikipedia-org-3337	188	19	equilibrium	equilibrium	NN
en-wikipedia-org-3337	188	20	in	in	IN
en-wikipedia-org-3337	188	21	every	every	DT
en-wikipedia-org-3337	188	22	subgame	subgame	NN
en-wikipedia-org-3337	188	23	of	of	IN
en-wikipedia-org-3337	188	24	that	that	DT
en-wikipedia-org-3337	188	25	game	game	NN
en-wikipedia-org-3337	188	26	.	.	.
en-wikipedia-org-3337	189	1	This	this	DT
en-wikipedia-org-3337	189	2	eliminates	eliminate	VBZ
en-wikipedia-org-3337	189	3	all	all	DT
en-wikipedia-org-3337	189	4	non	non	JJ
en-wikipedia-org-3337	189	5	-	-	JJ
en-wikipedia-org-3337	189	6	credible	credible	JJ
en-wikipedia-org-3337	189	7	threats	threat	NNS
en-wikipedia-org-3337	189	8	,	,	,
en-wikipedia-org-3337	189	9	that	that	RB
en-wikipedia-org-3337	189	10	is	is	RB
en-wikipedia-org-3337	189	11	,	,	,
en-wikipedia-org-3337	189	12	strategies	strategy	NNS
en-wikipedia-org-3337	189	13	that	that	WDT
en-wikipedia-org-3337	189	14	contain	contain	VBP
en-wikipedia-org-3337	189	15	non	non	JJ
en-wikipedia-org-3337	189	16	-	-	JJ
en-wikipedia-org-3337	189	17	rational	rational	JJ
en-wikipedia-org-3337	189	18	moves	move	NNS
en-wikipedia-org-3337	189	19	in	in	IN
en-wikipedia-org-3337	189	20	order	order	NN
en-wikipedia-org-3337	189	21	to	to	TO
en-wikipedia-org-3337	189	22	make	make	VB
en-wikipedia-org-3337	189	23	the	the	DT
en-wikipedia-org-3337	189	24	counter	counter	NN
en-wikipedia-org-3337	189	25	-	-	NN
en-wikipedia-org-3337	189	26	player	player	NN
en-wikipedia-org-3337	189	27	change	change	VB
en-wikipedia-org-3337	189	28	their	-PRON-	PRP$
en-wikipedia-org-3337	189	29	strategy	strategy	NN
en-wikipedia-org-3337	189	30	.	.	.
en-wikipedia-org-3337	190	1	The	the	DT
en-wikipedia-org-3337	190	2	image	image	NN
en-wikipedia-org-3337	190	3	to	to	IN
en-wikipedia-org-3337	190	4	the	the	DT
en-wikipedia-org-3337	190	5	right	right	NN
en-wikipedia-org-3337	190	6	shows	show	VBZ
en-wikipedia-org-3337	190	7	a	a	DT
en-wikipedia-org-3337	190	8	simple	simple	JJ
en-wikipedia-org-3337	190	9	sequential	sequential	JJ
en-wikipedia-org-3337	190	10	game	game	NN
en-wikipedia-org-3337	190	11	that	that	WDT
en-wikipedia-org-3337	190	12	illustrates	illustrate	VBZ
en-wikipedia-org-3337	190	13	the	the	DT
en-wikipedia-org-3337	190	14	issue	issue	NN
en-wikipedia-org-3337	190	15	with	with	IN
en-wikipedia-org-3337	190	16	subgame	subgame	NN
en-wikipedia-org-3337	190	17	imperfect	imperfect	JJ
en-wikipedia-org-3337	190	18	Nash	Nash	NNP
en-wikipedia-org-3337	190	19	equilibria	equilibria	NN
en-wikipedia-org-3337	190	20	.	.	.
en-wikipedia-org-3337	191	1	In	in	IN
en-wikipedia-org-3337	191	2	this	this	DT
en-wikipedia-org-3337	191	3	game	game	NN
en-wikipedia-org-3337	191	4	player	player	NN
en-wikipedia-org-3337	191	5	one	one	CD
en-wikipedia-org-3337	191	6	chooses	choose	VBZ
en-wikipedia-org-3337	191	7	left(L	left(l	$
en-wikipedia-org-3337	191	8	)	)	-RRB-
en-wikipedia-org-3337	191	9	or	or	CC
en-wikipedia-org-3337	191	10	right(R	right(r	XX
en-wikipedia-org-3337	191	11	)	)	-RRB-
en-wikipedia-org-3337	191	12	,	,	,
en-wikipedia-org-3337	191	13	which	which	WDT
en-wikipedia-org-3337	191	14	is	be	VBZ
en-wikipedia-org-3337	191	15	followed	follow	VBN
en-wikipedia-org-3337	191	16	by	by	IN
en-wikipedia-org-3337	191	17	player	player	NN
en-wikipedia-org-3337	191	18	two	two	CD
en-wikipedia-org-3337	191	19	being	be	VBG
en-wikipedia-org-3337	191	20	called	call	VBN
en-wikipedia-org-3337	191	21	upon	upon	IN
en-wikipedia-org-3337	191	22	to	to	TO
en-wikipedia-org-3337	191	23	be	be	VB
en-wikipedia-org-3337	191	24	kind	kind	JJ
en-wikipedia-org-3337	191	25	(	(	-LRB-
en-wikipedia-org-3337	191	26	K	K	NNP
en-wikipedia-org-3337	191	27	)	)	-RRB-
en-wikipedia-org-3337	191	28	or	or	CC
en-wikipedia-org-3337	191	29	unkind	unkind	JJ
en-wikipedia-org-3337	191	30	(	(	-LRB-
en-wikipedia-org-3337	191	31	U	u	NN
en-wikipedia-org-3337	191	32	)	)	-RRB-
en-wikipedia-org-3337	191	33	to	to	TO
en-wikipedia-org-3337	191	34	player	player	NN
en-wikipedia-org-3337	191	35	one	one	CD
en-wikipedia-org-3337	191	36	,	,	,
en-wikipedia-org-3337	191	37	However	however	RB
en-wikipedia-org-3337	191	38	,	,	,
en-wikipedia-org-3337	191	39	player	player	NN
en-wikipedia-org-3337	191	40	two	two	CD
en-wikipedia-org-3337	191	41	only	only	RB
en-wikipedia-org-3337	191	42	stands	stand	VBZ
en-wikipedia-org-3337	191	43	to	to	TO
en-wikipedia-org-3337	191	44	gain	gain	VB
en-wikipedia-org-3337	191	45	from	from	IN
en-wikipedia-org-3337	191	46	being	be	VBG
en-wikipedia-org-3337	191	47	unkind	unkind	JJ
en-wikipedia-org-3337	191	48	if	if	IN
en-wikipedia-org-3337	191	49	player	player	NN
en-wikipedia-org-3337	191	50	one	one	NN
en-wikipedia-org-3337	191	51	goes	go	VBZ
en-wikipedia-org-3337	191	52	left	leave	VBN
en-wikipedia-org-3337	191	53	.	.	.
en-wikipedia-org-3337	192	1	If	if	IN
en-wikipedia-org-3337	192	2	player	player	NN
en-wikipedia-org-3337	192	3	one	one	NN
en-wikipedia-org-3337	192	4	goes	go	VBZ
en-wikipedia-org-3337	192	5	right	right	IN
en-wikipedia-org-3337	192	6	the	the	DT
en-wikipedia-org-3337	192	7	rational	rational	JJ
en-wikipedia-org-3337	192	8	player	player	NN
en-wikipedia-org-3337	192	9	two	two	CD
en-wikipedia-org-3337	192	10	would	would	MD
en-wikipedia-org-3337	192	11	de	de	FW
en-wikipedia-org-3337	192	12	facto	facto	FW
en-wikipedia-org-3337	192	13	be	be	VB
en-wikipedia-org-3337	192	14	kind	kind	JJ
en-wikipedia-org-3337	192	15	to	to	IN
en-wikipedia-org-3337	192	16	her	-PRON-	PRP
en-wikipedia-org-3337	192	17	/	/	SYM
en-wikipedia-org-3337	192	18	him	-PRON-	PRP
en-wikipedia-org-3337	192	19	in	in	IN
en-wikipedia-org-3337	192	20	that	that	DT
en-wikipedia-org-3337	192	21	subgame	subgame	NN
en-wikipedia-org-3337	192	22	.	.	.
en-wikipedia-org-3337	193	1	However	however	RB
en-wikipedia-org-3337	193	2	,	,	,
en-wikipedia-org-3337	193	3	The	the	DT
en-wikipedia-org-3337	193	4	non	non	JJ
en-wikipedia-org-3337	193	5	-	-	JJ
en-wikipedia-org-3337	193	6	credible	credible	JJ
en-wikipedia-org-3337	193	7	threat	threat	NN
en-wikipedia-org-3337	193	8	of	of	IN
en-wikipedia-org-3337	193	9	being	be	VBG
en-wikipedia-org-3337	193	10	unkind	unkind	JJ
en-wikipedia-org-3337	193	11	at	at	IN
en-wikipedia-org-3337	193	12	2(2	2(2	NNP
en-wikipedia-org-3337	193	13	)	)	-RRB-
en-wikipedia-org-3337	193	14	is	be	VBZ
en-wikipedia-org-3337	193	15	still	still	RB
en-wikipedia-org-3337	193	16	part	part	NN
en-wikipedia-org-3337	193	17	of	of	IN
en-wikipedia-org-3337	193	18	the	the	DT
en-wikipedia-org-3337	193	19	blue	blue	JJ
en-wikipedia-org-3337	193	20	(	(	-LRB-
en-wikipedia-org-3337	193	21	L	l	NN
en-wikipedia-org-3337	193	22	,	,	,
en-wikipedia-org-3337	193	23	(	(	-LRB-
en-wikipedia-org-3337	193	24	U	u	NN
en-wikipedia-org-3337	193	25	,	,	,
en-wikipedia-org-3337	193	26	U	u	NN
en-wikipedia-org-3337	193	27	)	)	-RRB-
en-wikipedia-org-3337	193	28	)	)	-RRB-
en-wikipedia-org-3337	193	29	Nash	nash	JJ
en-wikipedia-org-3337	193	30	equilibrium	equilibrium	NN
en-wikipedia-org-3337	193	31	.	.	.
en-wikipedia-org-3337	194	1	Therefore	therefore	RB
en-wikipedia-org-3337	194	2	,	,	,
en-wikipedia-org-3337	194	3	if	if	IN
en-wikipedia-org-3337	194	4	rational	rational	JJ
en-wikipedia-org-3337	194	5	behavior	behavior	NN
en-wikipedia-org-3337	194	6	can	can	MD
en-wikipedia-org-3337	194	7	be	be	VB
en-wikipedia-org-3337	194	8	expected	expect	VBN
en-wikipedia-org-3337	194	9	by	by	IN
en-wikipedia-org-3337	194	10	both	both	DT
en-wikipedia-org-3337	194	11	parties	party	NNS
en-wikipedia-org-3337	194	12	the	the	DT
en-wikipedia-org-3337	194	13	subgame	subgame	NN
en-wikipedia-org-3337	194	14	perfect	perfect	JJ
en-wikipedia-org-3337	194	15	Nash	Nash	NNP
en-wikipedia-org-3337	194	16	equilibrium	equilibrium	NN
en-wikipedia-org-3337	194	17	may	may	MD
en-wikipedia-org-3337	194	18	be	be	VB
en-wikipedia-org-3337	194	19	a	a	DT
en-wikipedia-org-3337	194	20	more	more	RBR
en-wikipedia-org-3337	194	21	meaningful	meaningful	JJ
en-wikipedia-org-3337	194	22	solution	solution	NN
en-wikipedia-org-3337	194	23	concept	concept	NN
en-wikipedia-org-3337	194	24	when	when	WRB
en-wikipedia-org-3337	194	25	such	such	JJ
en-wikipedia-org-3337	194	26	dynamic	dynamic	JJ
en-wikipedia-org-3337	194	27	inconsistencies	inconsistency	NNS
en-wikipedia-org-3337	194	28	arise	arise	VBP
en-wikipedia-org-3337	194	29	.	.	.
en-wikipedia-org-3337	195	1	Proof	proof	NN
en-wikipedia-org-3337	195	2	of	of	IN
en-wikipedia-org-3337	195	3	existence[edit	existence[edit	NNP
en-wikipedia-org-3337	195	4	]	]	-RRB-
en-wikipedia-org-3337	195	5	Proof	Proof	NNP
en-wikipedia-org-3337	195	6	using	use	VBG
en-wikipedia-org-3337	195	7	the	the	DT
en-wikipedia-org-3337	195	8	Kakutani	Kakutani	NNP
en-wikipedia-org-3337	195	9	fixed	fix	VBN
en-wikipedia-org-3337	195	10	-	-	HYPH
en-wikipedia-org-3337	195	11	point	point	NN
en-wikipedia-org-3337	195	12	theorem[edit	theorem[edit	NFP
en-wikipedia-org-3337	195	13	]	]	-RRB-
en-wikipedia-org-3337	195	14	Nash	Nash	NNP
en-wikipedia-org-3337	195	15	's	's	POS
en-wikipedia-org-3337	195	16	original	original	JJ
en-wikipedia-org-3337	195	17	proof	proof	NN
en-wikipedia-org-3337	195	18	(	(	-LRB-
en-wikipedia-org-3337	195	19	in	in	IN
en-wikipedia-org-3337	195	20	his	-PRON-	PRP$
en-wikipedia-org-3337	195	21	thesis	thesis	NN
en-wikipedia-org-3337	195	22	)	)	-RRB-
en-wikipedia-org-3337	195	23	used	use	VBD
en-wikipedia-org-3337	195	24	Brouwer	Brouwer	NNP
en-wikipedia-org-3337	195	25	's	's	POS
en-wikipedia-org-3337	195	26	fixed	fix	VBN
en-wikipedia-org-3337	195	27	-	-	HYPH
en-wikipedia-org-3337	195	28	point	point	NN
en-wikipedia-org-3337	195	29	theorem	theorem	NN
en-wikipedia-org-3337	195	30	(	(	-LRB-
en-wikipedia-org-3337	195	31	e.g.	e.g.	RB
en-wikipedia-org-3337	195	32	,	,	,
en-wikipedia-org-3337	195	33	see	see	VB
en-wikipedia-org-3337	195	34	below	below	RB
en-wikipedia-org-3337	195	35	for	for	IN
en-wikipedia-org-3337	195	36	a	a	DT
en-wikipedia-org-3337	195	37	variant	variant	NN
en-wikipedia-org-3337	195	38	)	)	-RRB-
en-wikipedia-org-3337	195	39	.	.	.
en-wikipedia-org-3337	196	1	We	-PRON-	PRP
en-wikipedia-org-3337	196	2	give	give	VBP
en-wikipedia-org-3337	196	3	a	a	DT
en-wikipedia-org-3337	196	4	simpler	simple	JJR
en-wikipedia-org-3337	196	5	proof	proof	NN
en-wikipedia-org-3337	196	6	via	via	IN
en-wikipedia-org-3337	196	7	the	the	DT
en-wikipedia-org-3337	196	8	Kakutani	Kakutani	NNP
en-wikipedia-org-3337	196	9	fixed	fix	VBN
en-wikipedia-org-3337	196	10	-	-	HYPH
en-wikipedia-org-3337	196	11	point	point	NN
en-wikipedia-org-3337	196	12	theorem	theorem	NN
en-wikipedia-org-3337	196	13	,	,	,
en-wikipedia-org-3337	196	14	following	follow	VBG
en-wikipedia-org-3337	196	15	Nash	Nash	NNP
en-wikipedia-org-3337	196	16	's	's	POS
en-wikipedia-org-3337	196	17	1950	1950	CD
en-wikipedia-org-3337	196	18	paper	paper	NN
en-wikipedia-org-3337	196	19	(	(	-LRB-
en-wikipedia-org-3337	196	20	he	-PRON-	PRP
en-wikipedia-org-3337	196	21	credits	credit	VBZ
en-wikipedia-org-3337	196	22	David	David	NNP
en-wikipedia-org-3337	196	23	Gale	Gale	NNP
en-wikipedia-org-3337	196	24	with	with	IN
en-wikipedia-org-3337	196	25	the	the	DT
en-wikipedia-org-3337	196	26	observation	observation	NN
en-wikipedia-org-3337	196	27	that	that	IN
en-wikipedia-org-3337	196	28	such	such	PDT
en-wikipedia-org-3337	196	29	a	a	DT
en-wikipedia-org-3337	196	30	simplification	simplification	NN
en-wikipedia-org-3337	196	31	is	be	VBZ
en-wikipedia-org-3337	196	32	possible	possible	JJ
en-wikipedia-org-3337	196	33	)	)	-RRB-
en-wikipedia-org-3337	196	34	.	.	.
en-wikipedia-org-3337	197	1	To	to	TO
en-wikipedia-org-3337	197	2	prove	prove	VB
en-wikipedia-org-3337	197	3	the	the	DT
en-wikipedia-org-3337	197	4	existence	existence	NN
en-wikipedia-org-3337	197	5	of	of	IN
en-wikipedia-org-3337	197	6	a	a	DT
en-wikipedia-org-3337	197	7	Nash	Nash	NNP
en-wikipedia-org-3337	197	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	197	9	,	,	,
en-wikipedia-org-3337	197	10	let	let	VB
en-wikipedia-org-3337	197	11	r	r	NN
en-wikipedia-org-3337	197	12	i	i	PRP
en-wikipedia-org-3337	197	13	(	(	-LRB-
en-wikipedia-org-3337	197	14	σ	σ	NNP
en-wikipedia-org-3337	197	15	−	−	NNP
en-wikipedia-org-3337	197	16	i	i	NN
en-wikipedia-org-3337	197	17	)	)	-RRB-
en-wikipedia-org-3337	197	18	{	{	-LRB-
en-wikipedia-org-3337	197	19	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	197	20	r_{i}(\sigma	r_{i}(\sigma	NNP
en-wikipedia-org-3337	197	21	_	_	NNP
en-wikipedia-org-3337	197	22	{	{	-LRB-
en-wikipedia-org-3337	197	23	-i	-i	:
en-wikipedia-org-3337	197	24	}	}	-RRB-
en-wikipedia-org-3337	197	25	)	)	-RRB-
en-wikipedia-org-3337	197	26	}	}	-RRB-
en-wikipedia-org-3337	197	27	be	be	VB
en-wikipedia-org-3337	197	28	the	the	DT
en-wikipedia-org-3337	197	29	best	good	JJS
en-wikipedia-org-3337	197	30	response	response	NN
en-wikipedia-org-3337	197	31	of	of	IN
en-wikipedia-org-3337	197	32	player	player	NN
en-wikipedia-org-3337	197	33	i	i	PRP
en-wikipedia-org-3337	197	34	to	to	IN
en-wikipedia-org-3337	197	35	the	the	DT
en-wikipedia-org-3337	197	36	strategies	strategy	NNS
en-wikipedia-org-3337	197	37	of	of	IN
en-wikipedia-org-3337	197	38	all	all	DT
en-wikipedia-org-3337	197	39	other	other	JJ
en-wikipedia-org-3337	197	40	players	player	NNS
en-wikipedia-org-3337	197	41	.	.	.
en-wikipedia-org-3337	198	1	r	r	NNP
en-wikipedia-org-3337	198	2	i	i	NNP
en-wikipedia-org-3337	198	3	(	(	-LRB-
en-wikipedia-org-3337	198	4	σ	σ	NNP
en-wikipedia-org-3337	198	5	−	−	NNP
en-wikipedia-org-3337	198	6	i	i	NN
en-wikipedia-org-3337	198	7	)	)	-RRB-
en-wikipedia-org-3337	198	8	=	=	NFP
en-wikipedia-org-3337	198	9	a	a	DT
en-wikipedia-org-3337	198	10	r	r	NN
en-wikipedia-org-3337	198	11	g	g	NN
en-wikipedia-org-3337	198	12	m	m	NNP
en-wikipedia-org-3337	198	13	a	a	NN
en-wikipedia-org-3337	198	14	x	x	NN
en-wikipedia-org-3337	198	15	σ	σ	NN
en-wikipedia-org-3337	198	16	i	i	NN
en-wikipedia-org-3337	198	17	⁡	⁡	VBD
en-wikipedia-org-3337	198	18	u	u	NNP
en-wikipedia-org-3337	198	19	i	i	NN
en-wikipedia-org-3337	198	20	(	(	-LRB-
en-wikipedia-org-3337	198	21	σ	σ	NNP
en-wikipedia-org-3337	198	22	i	i	NN
en-wikipedia-org-3337	198	23	,	,	,
en-wikipedia-org-3337	198	24	σ	σ	NNP
en-wikipedia-org-3337	198	25	−	−	NNP
en-wikipedia-org-3337	198	26	i	i	NN
en-wikipedia-org-3337	198	27	)	)	-RRB-
en-wikipedia-org-3337	198	28	{	{	-LRB-
en-wikipedia-org-3337	198	29	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	198	30	r_{i}(\sigma	r_{i}(\sigma	VBN
en-wikipedia-org-3337	198	31	_	_	NNP
en-wikipedia-org-3337	198	32	{	{	-LRB-
en-wikipedia-org-3337	198	33	-i})=\mathop	-i})=\mathop	VB
en-wikipedia-org-3337	198	34	{	{	-LRB-
en-wikipedia-org-3337	198	35	\underset	\underset	CD
en-wikipedia-org-3337	198	36	{	{	-LRB-
en-wikipedia-org-3337	198	37	\sigma	\sigma	CD
en-wikipedia-org-3337	198	38	_	_	NNP
en-wikipedia-org-3337	198	39	{	{	-LRB-
en-wikipedia-org-3337	198	40	i}}{\operatorname	i}}{\operatorname	NNP
en-wikipedia-org-3337	198	41	{	{	-LRB-
en-wikipedia-org-3337	198	42	arg\,max	arg\,max	NN
en-wikipedia-org-3337	198	43	}	}	-RRB-
en-wikipedia-org-3337	198	44	}	}	-RRB-
en-wikipedia-org-3337	198	45	}	}	-RRB-
en-wikipedia-org-3337	198	46	u_{i}(\sigma	u_{i}(\sigma	NNP
en-wikipedia-org-3337	198	47	_	_	NNP
en-wikipedia-org-3337	198	48	{	{	-LRB-
en-wikipedia-org-3337	198	49	i},\sigma	i},\sigma	NNP
en-wikipedia-org-3337	198	50	_	_	NNP
en-wikipedia-org-3337	198	51	{	{	-LRB-
en-wikipedia-org-3337	198	52	-i	-i	:
en-wikipedia-org-3337	198	53	}	}	-RRB-
en-wikipedia-org-3337	198	54	)	)	-RRB-
en-wikipedia-org-3337	198	55	}	}	-RRB-
en-wikipedia-org-3337	198	56	Here	here	RB
en-wikipedia-org-3337	198	57	,	,	,
en-wikipedia-org-3337	198	58	σ	σ	VBZ
en-wikipedia-org-3337	198	59	∈	∈	NNP
en-wikipedia-org-3337	198	60	Σ	Σ	NNP
en-wikipedia-org-3337	198	61	{	{	-LRB-
en-wikipedia-org-3337	198	62	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	198	63	\sigma	\sigma	CD
en-wikipedia-org-3337	198	64	\in	\in	NNP
en-wikipedia-org-3337	198	65	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	198	66	}	}	-RRB-
en-wikipedia-org-3337	198	67	,	,	,
en-wikipedia-org-3337	198	68	where	where	WRB
en-wikipedia-org-3337	198	69	Σ	Σ	NNP
en-wikipedia-org-3337	198	70	=	=	SYM
en-wikipedia-org-3337	198	71	Σ	Σ	NNP
en-wikipedia-org-3337	198	72	i	i	PRP
en-wikipedia-org-3337	198	73	×	×	VBP
en-wikipedia-org-3337	198	74	Σ	Σ	NNP
en-wikipedia-org-3337	198	75	−	−	NNP
en-wikipedia-org-3337	198	76	i	i	PRP
en-wikipedia-org-3337	198	77	{	{	-LRB-
en-wikipedia-org-3337	198	78	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	198	79	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	198	80	=	=	SYM
en-wikipedia-org-3337	198	81	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	198	82	_	_	NNP
en-wikipedia-org-3337	198	83	{	{	-LRB-
en-wikipedia-org-3337	198	84	i}\times	i}\times	NN
en-wikipedia-org-3337	198	85	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	198	86	_	_	NNP
en-wikipedia-org-3337	198	87	{	{	-LRB-
en-wikipedia-org-3337	198	88	-i	-i	:
en-wikipedia-org-3337	198	89	}	}	-RRB-
en-wikipedia-org-3337	198	90	}	}	-RRB-
en-wikipedia-org-3337	198	91	,	,	,
en-wikipedia-org-3337	198	92	is	be	VBZ
en-wikipedia-org-3337	198	93	a	a	DT
en-wikipedia-org-3337	198	94	mixed	mixed	JJ
en-wikipedia-org-3337	198	95	-	-	HYPH
en-wikipedia-org-3337	198	96	strategy	strategy	NN
en-wikipedia-org-3337	198	97	profile	profile	NN
en-wikipedia-org-3337	198	98	in	in	IN
en-wikipedia-org-3337	198	99	the	the	DT
en-wikipedia-org-3337	198	100	set	set	NN
en-wikipedia-org-3337	198	101	of	of	IN
en-wikipedia-org-3337	198	102	all	all	DT
en-wikipedia-org-3337	198	103	mixed	mix	VBN
en-wikipedia-org-3337	198	104	strategies	strategy	NNS
en-wikipedia-org-3337	198	105	and	and	CC
en-wikipedia-org-3337	198	106	u	u	LS
en-wikipedia-org-3337	198	107	i	i	NN
en-wikipedia-org-3337	198	108	{	{	-LRB-
en-wikipedia-org-3337	198	109	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	198	110	u_{i	u_{i	NN
en-wikipedia-org-3337	198	111	}	}	-RRB-
en-wikipedia-org-3337	198	112	}	}	-RRB-
en-wikipedia-org-3337	198	113	is	be	VBZ
en-wikipedia-org-3337	198	114	the	the	DT
en-wikipedia-org-3337	198	115	payoff	payoff	NN
en-wikipedia-org-3337	198	116	function	function	NN
en-wikipedia-org-3337	198	117	for	for	IN
en-wikipedia-org-3337	198	118	player	player	NN
en-wikipedia-org-3337	198	119	i.	i.	NNP
en-wikipedia-org-3337	199	1	Define	define	VB
en-wikipedia-org-3337	199	2	a	a	DT
en-wikipedia-org-3337	199	3	set	set	NN
en-wikipedia-org-3337	199	4	-	-	HYPH
en-wikipedia-org-3337	199	5	valued	value	VBN
en-wikipedia-org-3337	199	6	function	function	NN
en-wikipedia-org-3337	199	7	r	r	NN
en-wikipedia-org-3337	199	8	:	:	:
en-wikipedia-org-3337	199	9	Σ	σ	NN
en-wikipedia-org-3337	199	10	→	→	SYM
en-wikipedia-org-3337	199	11	2	2	CD
en-wikipedia-org-3337	199	12	Σ	σ	NN
en-wikipedia-org-3337	199	13	{	{	-LRB-
en-wikipedia-org-3337	199	14	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	199	15	r\colon	r\colon	NN
en-wikipedia-org-3337	199	16	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	199	17	\rightarrow	\rightarrow	CD
en-wikipedia-org-3337	199	18	2^{\Sigma	2^{\sigma	CD
en-wikipedia-org-3337	199	19	}	}	-RRB-
en-wikipedia-org-3337	199	20	}	}	-RRB-
en-wikipedia-org-3337	199	21	such	such	JJ
en-wikipedia-org-3337	199	22	that	that	IN
en-wikipedia-org-3337	199	23	r	r	NN
en-wikipedia-org-3337	199	24	=	=	SYM
en-wikipedia-org-3337	199	25	r	r	NN
en-wikipedia-org-3337	199	26	i	i	NN
en-wikipedia-org-3337	199	27	(	(	-LRB-
en-wikipedia-org-3337	199	28	σ	σ	NNP
en-wikipedia-org-3337	199	29	−	−	NNP
en-wikipedia-org-3337	199	30	i	i	NN
en-wikipedia-org-3337	199	31	)	)	-RRB-
en-wikipedia-org-3337	199	32	×	×	ADD
en-wikipedia-org-3337	199	33	r	r	NN
en-wikipedia-org-3337	199	34	−	−	NNP
en-wikipedia-org-3337	199	35	i	i	PRP
en-wikipedia-org-3337	199	36	(	(	-LRB-
en-wikipedia-org-3337	199	37	σ	σ	NNP
en-wikipedia-org-3337	199	38	i	i	NN
en-wikipedia-org-3337	199	39	)	)	-RRB-
en-wikipedia-org-3337	199	40	{	{	-LRB-
en-wikipedia-org-3337	199	41	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	199	42	r	r	NN
en-wikipedia-org-3337	199	43	=	=	SYM
en-wikipedia-org-3337	199	44	r_{i}(\sigma	r_{i}(\sigma	NNP
en-wikipedia-org-3337	199	45	_	_	NNP
en-wikipedia-org-3337	199	46	{	{	-LRB-
en-wikipedia-org-3337	199	47	-i})\times	-i})\times	NNP
en-wikipedia-org-3337	199	48	r_{-i}(\sigma	r_{-i}(\sigma	NNP
en-wikipedia-org-3337	199	49	_	_	NNP
en-wikipedia-org-3337	199	50	{	{	-LRB-
en-wikipedia-org-3337	199	51	i	i	NN
en-wikipedia-org-3337	199	52	}	}	-RRB-
en-wikipedia-org-3337	199	53	)	)	-RRB-
en-wikipedia-org-3337	199	54	}	}	-RRB-
en-wikipedia-org-3337	199	55	.	.	.
en-wikipedia-org-3337	200	1	The	the	DT
en-wikipedia-org-3337	200	2	existence	existence	NN
en-wikipedia-org-3337	200	3	of	of	IN
en-wikipedia-org-3337	200	4	a	a	DT
en-wikipedia-org-3337	200	5	Nash	Nash	NNP
en-wikipedia-org-3337	200	6	equilibrium	equilibrium	NN
en-wikipedia-org-3337	200	7	is	be	VBZ
en-wikipedia-org-3337	200	8	equivalent	equivalent	JJ
en-wikipedia-org-3337	200	9	to	to	IN
en-wikipedia-org-3337	200	10	r	r	NN
en-wikipedia-org-3337	200	11	{	{	-LRB-
en-wikipedia-org-3337	200	12	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	200	13	r	r	NN
en-wikipedia-org-3337	200	14	}	}	-RRB-
en-wikipedia-org-3337	200	15	having	have	VBG
en-wikipedia-org-3337	200	16	a	a	DT
en-wikipedia-org-3337	200	17	fixed	fix	VBN
en-wikipedia-org-3337	200	18	point	point	NN
en-wikipedia-org-3337	200	19	.	.	.
en-wikipedia-org-3337	201	1	Kakutani	Kakutani	NNP
en-wikipedia-org-3337	201	2	's	's	POS
en-wikipedia-org-3337	201	3	fixed	fix	VBN
en-wikipedia-org-3337	201	4	point	point	NN
en-wikipedia-org-3337	201	5	theorem	theorem	NN
en-wikipedia-org-3337	201	6	guarantees	guarantee	VBZ
en-wikipedia-org-3337	201	7	the	the	DT
en-wikipedia-org-3337	201	8	existence	existence	NN
en-wikipedia-org-3337	201	9	of	of	IN
en-wikipedia-org-3337	201	10	a	a	DT
en-wikipedia-org-3337	201	11	fixed	fix	VBN
en-wikipedia-org-3337	201	12	point	point	NN
en-wikipedia-org-3337	201	13	if	if	IN
en-wikipedia-org-3337	201	14	the	the	DT
en-wikipedia-org-3337	201	15	following	follow	VBG
en-wikipedia-org-3337	201	16	four	four	CD
en-wikipedia-org-3337	201	17	conditions	condition	NNS
en-wikipedia-org-3337	201	18	are	be	VBP
en-wikipedia-org-3337	201	19	satisfied	satisfied	JJ
en-wikipedia-org-3337	201	20	.	.	.
en-wikipedia-org-3337	202	1	Σ	Σ	NNP
en-wikipedia-org-3337	202	2	{	{	-LRB-
en-wikipedia-org-3337	202	3	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	202	4	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	202	5	}	}	-RRB-
en-wikipedia-org-3337	202	6	is	be	VBZ
en-wikipedia-org-3337	202	7	compact	compact	JJ
en-wikipedia-org-3337	202	8	,	,	,
en-wikipedia-org-3337	202	9	convex	convex	NNS
en-wikipedia-org-3337	202	10	,	,	,
en-wikipedia-org-3337	202	11	and	and	CC
en-wikipedia-org-3337	202	12	nonempty	nonempty	NNP
en-wikipedia-org-3337	202	13	.	.	.
en-wikipedia-org-3337	203	1	r	r	LS
en-wikipedia-org-3337	203	2	(	(	-LRB-
en-wikipedia-org-3337	203	3	σ	σ	NNP
en-wikipedia-org-3337	203	4	)	)	-RRB-
en-wikipedia-org-3337	203	5	{	{	-LRB-
en-wikipedia-org-3337	203	6	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	203	7	r(\sigma	r(\sigma	NNP
en-wikipedia-org-3337	203	8	)	)	-RRB-
en-wikipedia-org-3337	203	9	}	}	-RRB-
en-wikipedia-org-3337	203	10	is	be	VBZ
en-wikipedia-org-3337	203	11	nonempty	nonempty	JJ
en-wikipedia-org-3337	203	12	.	.	.
en-wikipedia-org-3337	204	1	r	r	LS
en-wikipedia-org-3337	204	2	(	(	-LRB-
en-wikipedia-org-3337	204	3	σ	σ	NNP
en-wikipedia-org-3337	204	4	)	)	-RRB-
en-wikipedia-org-3337	204	5	{	{	-LRB-
en-wikipedia-org-3337	204	6	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	204	7	r(\sigma	r(\sigma	NNP
en-wikipedia-org-3337	204	8	)	)	-RRB-
en-wikipedia-org-3337	204	9	}	}	-RRB-
en-wikipedia-org-3337	204	10	is	be	VBZ
en-wikipedia-org-3337	204	11	upper	upper	JJ
en-wikipedia-org-3337	204	12	hemicontinuous	hemicontinuous	JJ
en-wikipedia-org-3337	204	13	r	r	NN
en-wikipedia-org-3337	204	14	(	(	-LRB-
en-wikipedia-org-3337	204	15	σ	σ	NN
en-wikipedia-org-3337	204	16	)	)	-RRB-
en-wikipedia-org-3337	204	17	{	{	-LRB-
en-wikipedia-org-3337	204	18	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	204	19	r(\sigma	r(\sigma	NNP
en-wikipedia-org-3337	204	20	)	)	-RRB-
en-wikipedia-org-3337	204	21	}	}	-RRB-
en-wikipedia-org-3337	204	22	is	be	VBZ
en-wikipedia-org-3337	204	23	convex	convex	NNP
en-wikipedia-org-3337	204	24	.	.	.
en-wikipedia-org-3337	205	1	Condition	condition	NN
en-wikipedia-org-3337	205	2	1	1	CD
en-wikipedia-org-3337	205	3	.	.	.
en-wikipedia-org-3337	205	4	is	be	VBZ
en-wikipedia-org-3337	205	5	satisfied	satisfied	JJ
en-wikipedia-org-3337	205	6	from	from	IN
en-wikipedia-org-3337	205	7	the	the	DT
en-wikipedia-org-3337	205	8	fact	fact	NN
en-wikipedia-org-3337	205	9	that	that	IN
en-wikipedia-org-3337	205	10	Σ	Σ	NNP
en-wikipedia-org-3337	205	11	{	{	-LRB-
en-wikipedia-org-3337	205	12	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	205	13	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	205	14	}	}	-RRB-
en-wikipedia-org-3337	205	15	is	be	VBZ
en-wikipedia-org-3337	205	16	a	a	DT
en-wikipedia-org-3337	205	17	simplex	simplex	NN
en-wikipedia-org-3337	205	18	and	and	CC
en-wikipedia-org-3337	205	19	thus	thus	RB
en-wikipedia-org-3337	205	20	compact	compact	JJ
en-wikipedia-org-3337	205	21	.	.	.
en-wikipedia-org-3337	206	1	Convexity	convexity	NN
en-wikipedia-org-3337	206	2	follows	follow	VBZ
en-wikipedia-org-3337	206	3	from	from	IN
en-wikipedia-org-3337	206	4	players	player	NNS
en-wikipedia-org-3337	206	5	'	'	POS
en-wikipedia-org-3337	206	6	ability	ability	NN
en-wikipedia-org-3337	206	7	to	to	TO
en-wikipedia-org-3337	206	8	mix	mix	VB
en-wikipedia-org-3337	206	9	strategies	strategy	NNS
en-wikipedia-org-3337	206	10	.	.	.
en-wikipedia-org-3337	207	1	Σ	Σ	NNP
en-wikipedia-org-3337	207	2	{	{	-LRB-
en-wikipedia-org-3337	207	3	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	207	4	\Sigma	\Sigma	NNP
en-wikipedia-org-3337	207	5	}	}	-RRB-
en-wikipedia-org-3337	207	6	is	be	VBZ
en-wikipedia-org-3337	207	7	nonempty	nonempty	JJ
en-wikipedia-org-3337	207	8	as	as	RB
en-wikipedia-org-3337	207	9	long	long	RB
en-wikipedia-org-3337	207	10	as	as	IN
en-wikipedia-org-3337	207	11	players	player	NNS
en-wikipedia-org-3337	207	12	have	have	VBP
en-wikipedia-org-3337	207	13	strategies	strategy	NNS
en-wikipedia-org-3337	207	14	.	.	.
en-wikipedia-org-3337	208	1	Condition	condition	NN
en-wikipedia-org-3337	208	2	2	2	CD
en-wikipedia-org-3337	208	3	.	.	.
en-wikipedia-org-3337	208	4	and	and	CC
en-wikipedia-org-3337	208	5	3	3	CD
en-wikipedia-org-3337	208	6	.	.	.
en-wikipedia-org-3337	208	7	are	be	VBP
en-wikipedia-org-3337	208	8	satisfied	satisfied	JJ
en-wikipedia-org-3337	208	9	by	by	IN
en-wikipedia-org-3337	208	10	way	way	NN
en-wikipedia-org-3337	208	11	of	of	IN
en-wikipedia-org-3337	208	12	Berge	Berge	NNP
en-wikipedia-org-3337	208	13	's	's	POS
en-wikipedia-org-3337	208	14	maximum	maximum	JJ
en-wikipedia-org-3337	208	15	theorem	theorem	NN
en-wikipedia-org-3337	208	16	.	.	.
en-wikipedia-org-3337	209	1	Because	because	IN
en-wikipedia-org-3337	209	2	u	u	PRP
en-wikipedia-org-3337	209	3	i	i	NN
en-wikipedia-org-3337	209	4	{	{	-LRB-
en-wikipedia-org-3337	209	5	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	209	6	u_{i	u_{i	NN
en-wikipedia-org-3337	209	7	}	}	-RRB-
en-wikipedia-org-3337	209	8	}	}	-RRB-
en-wikipedia-org-3337	209	9	is	be	VBZ
en-wikipedia-org-3337	209	10	continuous	continuous	JJ
en-wikipedia-org-3337	209	11	and	and	CC
en-wikipedia-org-3337	209	12	compact	compact	JJ
en-wikipedia-org-3337	209	13	,	,	,
en-wikipedia-org-3337	209	14	r	r	LS
en-wikipedia-org-3337	209	15	(	(	-LRB-
en-wikipedia-org-3337	209	16	σ	σ	NNP
en-wikipedia-org-3337	209	17	i	i	NN
en-wikipedia-org-3337	209	18	)	)	-RRB-
en-wikipedia-org-3337	209	19	{	{	-LRB-
en-wikipedia-org-3337	209	20	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	209	21	r(\sigma	r(\sigma	NNP
en-wikipedia-org-3337	209	22	_	_	NNP
en-wikipedia-org-3337	209	23	{	{	-LRB-
en-wikipedia-org-3337	209	24	i	i	NN
en-wikipedia-org-3337	209	25	}	}	-RRB-
en-wikipedia-org-3337	209	26	)	)	-RRB-
en-wikipedia-org-3337	209	27	}	}	-RRB-
en-wikipedia-org-3337	209	28	is	be	VBZ
en-wikipedia-org-3337	209	29	non	non	JJ
en-wikipedia-org-3337	209	30	-	-	JJ
en-wikipedia-org-3337	209	31	empty	empty	JJ
en-wikipedia-org-3337	209	32	and	and	CC
en-wikipedia-org-3337	209	33	upper	upper	JJ
en-wikipedia-org-3337	209	34	hemicontinuous	hemicontinuous	JJ
en-wikipedia-org-3337	209	35	.	.	.
en-wikipedia-org-3337	210	1	Condition	condition	NN
en-wikipedia-org-3337	210	2	4	4	CD
en-wikipedia-org-3337	210	3	.	.	.
en-wikipedia-org-3337	210	4	is	be	VBZ
en-wikipedia-org-3337	210	5	satisfied	satisfied	JJ
en-wikipedia-org-3337	210	6	as	as	IN
en-wikipedia-org-3337	210	7	a	a	DT
en-wikipedia-org-3337	210	8	result	result	NN
en-wikipedia-org-3337	210	9	of	of	IN
en-wikipedia-org-3337	210	10	mixed	mixed	JJ
en-wikipedia-org-3337	210	11	strategies	strategy	NNS
en-wikipedia-org-3337	210	12	.	.	.
en-wikipedia-org-3337	211	1	Suppose	suppose	VB
en-wikipedia-org-3337	211	2	σ	σ	NNP
en-wikipedia-org-3337	211	3	i	i	NN
en-wikipedia-org-3337	211	4	,	,	,
en-wikipedia-org-3337	211	5	σ	σ	NNP
en-wikipedia-org-3337	211	6	i	i	NN
en-wikipedia-org-3337	211	7	′	′	.
en-wikipedia-org-3337	211	8	∈	∈	NNP
en-wikipedia-org-3337	211	9	r	r	NN
en-wikipedia-org-3337	211	10	(	(	-LRB-
en-wikipedia-org-3337	211	11	σ	σ	NNP
en-wikipedia-org-3337	211	12	−	−	NNP
en-wikipedia-org-3337	211	13	i	i	NN
en-wikipedia-org-3337	211	14	)	)	-RRB-
en-wikipedia-org-3337	211	15	{	{	-LRB-
en-wikipedia-org-3337	211	16	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	211	17	\sigma	\sigma	CD
en-wikipedia-org-3337	211	18	_	_	NNP
en-wikipedia-org-3337	211	19	{	{	-LRB-
en-wikipedia-org-3337	211	20	i},\sigma	i},\sigma	NNP
en-wikipedia-org-3337	211	21	'	'	``
en-wikipedia-org-3337	211	22	_	_	NNP
en-wikipedia-org-3337	211	23	{	{	-LRB-
en-wikipedia-org-3337	211	24	i}\in	i}\in	NNP
en-wikipedia-org-3337	211	25	r(\sigma	r(\sigma	NNP
en-wikipedia-org-3337	211	26	_	_	NNP
en-wikipedia-org-3337	211	27	{	{	-LRB-
en-wikipedia-org-3337	211	28	-i	-i	:
en-wikipedia-org-3337	211	29	}	}	-RRB-
en-wikipedia-org-3337	211	30	)	)	-RRB-
en-wikipedia-org-3337	211	31	}	}	-RRB-
en-wikipedia-org-3337	211	32	,	,	,
en-wikipedia-org-3337	211	33	then	then	RB
en-wikipedia-org-3337	211	34	λ	λ	NNP
en-wikipedia-org-3337	211	35	σ	σ	XX
en-wikipedia-org-3337	211	36	i	i	NN
en-wikipedia-org-3337	211	37	+	+	CC
en-wikipedia-org-3337	211	38	(	(	-LRB-
en-wikipedia-org-3337	211	39	1	1	CD
en-wikipedia-org-3337	211	40	−	−	NNP
en-wikipedia-org-3337	211	41	λ	λ	NNP
en-wikipedia-org-3337	211	42	)	)	-RRB-
en-wikipedia-org-3337	211	43	σ	σ	NN
en-wikipedia-org-3337	211	44	i	i	NN
en-wikipedia-org-3337	211	45	′	′	.
en-wikipedia-org-3337	211	46	∈	∈	NNP
en-wikipedia-org-3337	211	47	r	r	NN
en-wikipedia-org-3337	211	48	(	(	-LRB-
en-wikipedia-org-3337	211	49	σ	σ	NNP
en-wikipedia-org-3337	211	50	−	−	NNP
en-wikipedia-org-3337	211	51	i	i	NN
en-wikipedia-org-3337	211	52	)	)	-RRB-
en-wikipedia-org-3337	211	53	{	{	-LRB-
en-wikipedia-org-3337	211	54	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	211	55	\lambda	\lambda	CD
en-wikipedia-org-3337	211	56	\sigma	\sigma	CD
en-wikipedia-org-3337	211	57	_	_	NNP
en-wikipedia-org-3337	211	58	{	{	-LRB-
en-wikipedia-org-3337	211	59	i}+(1-\lambda	i}+(1-\lambda	NN
en-wikipedia-org-3337	211	60	)	)	-RRB-
en-wikipedia-org-3337	211	61	\sigma	\sigma	NNP
en-wikipedia-org-3337	211	62	'	'	``
en-wikipedia-org-3337	211	63	_	_	NNP
en-wikipedia-org-3337	211	64	{	{	-LRB-
en-wikipedia-org-3337	211	65	i}\in	i}\in	NNP
en-wikipedia-org-3337	211	66	r(\sigma	r(\sigma	NNP
en-wikipedia-org-3337	211	67	_	_	NNP
en-wikipedia-org-3337	211	68	{	{	-LRB-
en-wikipedia-org-3337	211	69	-i	-i	:
en-wikipedia-org-3337	211	70	}	}	-RRB-
en-wikipedia-org-3337	211	71	)	)	-RRB-
en-wikipedia-org-3337	211	72	}	}	-RRB-
en-wikipedia-org-3337	211	73	.	.	.
en-wikipedia-org-3337	212	1	i.e.	i.e.	FW
en-wikipedia-org-3337	213	1	if	if	IN
en-wikipedia-org-3337	213	2	two	two	CD
en-wikipedia-org-3337	213	3	strategies	strategy	NNS
en-wikipedia-org-3337	213	4	maximize	maximize	VBP
en-wikipedia-org-3337	213	5	payoffs	payoff	NNS
en-wikipedia-org-3337	213	6	,	,	,
en-wikipedia-org-3337	213	7	then	then	RB
en-wikipedia-org-3337	213	8	a	a	DT
en-wikipedia-org-3337	213	9	mix	mix	NN
en-wikipedia-org-3337	213	10	between	between	IN
en-wikipedia-org-3337	213	11	the	the	DT
en-wikipedia-org-3337	213	12	two	two	CD
en-wikipedia-org-3337	213	13	strategies	strategy	NNS
en-wikipedia-org-3337	213	14	will	will	MD
en-wikipedia-org-3337	213	15	yield	yield	VB
en-wikipedia-org-3337	213	16	the	the	DT
en-wikipedia-org-3337	213	17	same	same	JJ
en-wikipedia-org-3337	213	18	payoff	payoff	NN
en-wikipedia-org-3337	213	19	.	.	.
en-wikipedia-org-3337	214	1	Therefore	therefore	RB
en-wikipedia-org-3337	214	2	,	,	,
en-wikipedia-org-3337	214	3	there	there	EX
en-wikipedia-org-3337	214	4	exists	exist	VBZ
en-wikipedia-org-3337	214	5	a	a	DT
en-wikipedia-org-3337	214	6	fixed	fix	VBN
en-wikipedia-org-3337	214	7	point	point	NN
en-wikipedia-org-3337	214	8	in	in	IN
en-wikipedia-org-3337	214	9	r	r	NN
en-wikipedia-org-3337	214	10	{	{	-LRB-
en-wikipedia-org-3337	214	11	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	214	12	r	r	NN
en-wikipedia-org-3337	214	13	}	}	-RRB-
en-wikipedia-org-3337	214	14	and	and	CC
en-wikipedia-org-3337	214	15	a	a	DT
en-wikipedia-org-3337	214	16	Nash	Nash	NNP
en-wikipedia-org-3337	214	17	equilibrium	equilibrium	NN
en-wikipedia-org-3337	214	18	.	.	.
en-wikipedia-org-3337	215	1	[	[	-LRB-
en-wikipedia-org-3337	215	2	22	22	CD
en-wikipedia-org-3337	215	3	]	]	-RRB-
en-wikipedia-org-3337	215	4	When	when	WRB
en-wikipedia-org-3337	215	5	Nash	Nash	NNP
en-wikipedia-org-3337	215	6	made	make	VBD
en-wikipedia-org-3337	215	7	this	this	DT
en-wikipedia-org-3337	215	8	point	point	NN
en-wikipedia-org-3337	215	9	to	to	IN
en-wikipedia-org-3337	215	10	John	John	NNP
en-wikipedia-org-3337	215	11	von	von	NNP
en-wikipedia-org-3337	215	12	Neumann	Neumann	NNP
en-wikipedia-org-3337	215	13	in	in	IN
en-wikipedia-org-3337	215	14	1949	1949	CD
en-wikipedia-org-3337	215	15	,	,	,
en-wikipedia-org-3337	215	16	von	von	NNP
en-wikipedia-org-3337	215	17	Neumann	Neumann	NNP
en-wikipedia-org-3337	215	18	famously	famously	RB
en-wikipedia-org-3337	215	19	dismissed	dismiss	VBD
en-wikipedia-org-3337	215	20	it	-PRON-	PRP
en-wikipedia-org-3337	215	21	with	with	IN
en-wikipedia-org-3337	215	22	the	the	DT
en-wikipedia-org-3337	215	23	words	word	NNS
en-wikipedia-org-3337	215	24	,	,	,
en-wikipedia-org-3337	215	25	"	"	``
en-wikipedia-org-3337	215	26	That	that	DT
en-wikipedia-org-3337	215	27	's	be	VBZ
en-wikipedia-org-3337	215	28	trivial	trivial	JJ
en-wikipedia-org-3337	215	29	,	,	,
en-wikipedia-org-3337	215	30	you	-PRON-	PRP
en-wikipedia-org-3337	215	31	know	know	VBP
en-wikipedia-org-3337	215	32	.	.	.
en-wikipedia-org-3337	216	1	That	that	DT
en-wikipedia-org-3337	216	2	's	be	VBZ
en-wikipedia-org-3337	216	3	just	just	RB
en-wikipedia-org-3337	216	4	a	a	DT
en-wikipedia-org-3337	216	5	fixed	fix	VBN
en-wikipedia-org-3337	216	6	-	-	HYPH
en-wikipedia-org-3337	216	7	point	point	NN
en-wikipedia-org-3337	216	8	theorem	theorem	NN
en-wikipedia-org-3337	216	9	.	.	.
en-wikipedia-org-3337	216	10	"	"	''
en-wikipedia-org-3337	217	1	(	(	-LRB-
en-wikipedia-org-3337	217	2	See	see	VB
en-wikipedia-org-3337	217	3	Nasar	Nasar	NNP
en-wikipedia-org-3337	217	4	,	,	,
en-wikipedia-org-3337	217	5	1998	1998	CD
en-wikipedia-org-3337	217	6	,	,	,
en-wikipedia-org-3337	217	7	p.	p.	NN
en-wikipedia-org-3337	218	1	94	94	CD
en-wikipedia-org-3337	218	2	.	.	.
en-wikipedia-org-3337	218	3	)	)	-RRB-
en-wikipedia-org-3337	219	1	Alternate	alternate	JJ
en-wikipedia-org-3337	219	2	proof	proof	NN
en-wikipedia-org-3337	219	3	using	use	VBG
en-wikipedia-org-3337	219	4	the	the	DT
en-wikipedia-org-3337	219	5	Brouwer	Brouwer	NNP
en-wikipedia-org-3337	219	6	fixed	fix	VBN
en-wikipedia-org-3337	219	7	-	-	HYPH
en-wikipedia-org-3337	219	8	point	point	NN
en-wikipedia-org-3337	219	9	theorem[edit	theorem[edit	LS
en-wikipedia-org-3337	219	10	]	]	-RRB-
en-wikipedia-org-3337	219	11	We	-PRON-	PRP
en-wikipedia-org-3337	219	12	have	have	VBP
en-wikipedia-org-3337	219	13	a	a	DT
en-wikipedia-org-3337	219	14	game	game	NN
en-wikipedia-org-3337	219	15	G	g	NN
en-wikipedia-org-3337	219	16	=	=	NFP
en-wikipedia-org-3337	219	17	(	(	-LRB-
en-wikipedia-org-3337	219	18	N	n	NN
en-wikipedia-org-3337	219	19	,	,	,
en-wikipedia-org-3337	219	20	A	a	NN
en-wikipedia-org-3337	219	21	,	,	,
en-wikipedia-org-3337	219	22	u	u	NN
en-wikipedia-org-3337	219	23	)	)	-RRB-
en-wikipedia-org-3337	219	24	{	{	-LRB-
en-wikipedia-org-3337	219	25	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	219	26	G=(N	g=(n	NN
en-wikipedia-org-3337	219	27	,	,	,
en-wikipedia-org-3337	219	28	A	a	NN
en-wikipedia-org-3337	219	29	,	,	,
en-wikipedia-org-3337	219	30	u	u	NNP
en-wikipedia-org-3337	219	31	)	)	-RRB-
en-wikipedia-org-3337	219	32	}	}	-RRB-
en-wikipedia-org-3337	219	33	where	where	WRB
en-wikipedia-org-3337	219	34	N	n	NN
en-wikipedia-org-3337	219	35	{	{	-LRB-
en-wikipedia-org-3337	219	36	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	219	37	N	n	NN
en-wikipedia-org-3337	219	38	}	}	-RRB-
en-wikipedia-org-3337	219	39	is	be	VBZ
en-wikipedia-org-3337	219	40	the	the	DT
en-wikipedia-org-3337	219	41	number	number	NN
en-wikipedia-org-3337	219	42	of	of	IN
en-wikipedia-org-3337	219	43	players	player	NNS
en-wikipedia-org-3337	219	44	and	and	CC
en-wikipedia-org-3337	219	45	A	a	NN
en-wikipedia-org-3337	219	46	=	=	SYM
en-wikipedia-org-3337	219	47	A	a	NN
en-wikipedia-org-3337	219	48	1	1	CD
en-wikipedia-org-3337	219	49	×	×	CD
en-wikipedia-org-3337	219	50	⋯	⋯	NNP
en-wikipedia-org-3337	219	51	×	×	CD
en-wikipedia-org-3337	219	52	A	a	NN
en-wikipedia-org-3337	219	53	N	n	CD
en-wikipedia-org-3337	219	54	{	{	-LRB-
en-wikipedia-org-3337	219	55	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	219	56	A	a	NN
en-wikipedia-org-3337	219	57	=	=	SYM
en-wikipedia-org-3337	219	58	A_{1}\times	a_{1}\times	NN
en-wikipedia-org-3337	219	59	\cdots	\cdots	CD
en-wikipedia-org-3337	219	60	\times	\times	CD
en-wikipedia-org-3337	219	61	A_{N	a_{n	NN
en-wikipedia-org-3337	219	62	}	}	-RRB-
en-wikipedia-org-3337	219	63	}	}	-RRB-
en-wikipedia-org-3337	219	64	is	be	VBZ
en-wikipedia-org-3337	219	65	the	the	DT
en-wikipedia-org-3337	219	66	action	action	NN
en-wikipedia-org-3337	219	67	set	set	VBN
en-wikipedia-org-3337	219	68	for	for	IN
en-wikipedia-org-3337	219	69	the	the	DT
en-wikipedia-org-3337	219	70	players	player	NNS
en-wikipedia-org-3337	219	71	.	.	.
en-wikipedia-org-3337	220	1	All	all	DT
en-wikipedia-org-3337	220	2	of	of	IN
en-wikipedia-org-3337	220	3	the	the	DT
en-wikipedia-org-3337	220	4	action	action	NN
en-wikipedia-org-3337	220	5	sets	set	VBZ
en-wikipedia-org-3337	220	6	A	a	DT
en-wikipedia-org-3337	220	7	i	i	NN
en-wikipedia-org-3337	220	8	{	{	-LRB-
en-wikipedia-org-3337	220	9	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	220	10	A_{i	a_{i	NN
en-wikipedia-org-3337	220	11	}	}	-RRB-
en-wikipedia-org-3337	220	12	}	}	-RRB-
en-wikipedia-org-3337	220	13	are	be	VBP
en-wikipedia-org-3337	220	14	finite	finite	JJ
en-wikipedia-org-3337	220	15	.	.	.
en-wikipedia-org-3337	221	1	Let	let	VB
en-wikipedia-org-3337	221	2	Δ	Δ	NNP
en-wikipedia-org-3337	221	3	=	=	SYM
en-wikipedia-org-3337	221	4	Δ	δ	NN
en-wikipedia-org-3337	221	5	1	1	CD
en-wikipedia-org-3337	221	6	×	×	CD
en-wikipedia-org-3337	221	7	⋯	⋯	NNP
en-wikipedia-org-3337	221	8	×	×	NN
en-wikipedia-org-3337	221	9	Δ	δ	NN
en-wikipedia-org-3337	221	10	N	n	CD
en-wikipedia-org-3337	221	11	{	{	-LRB-
en-wikipedia-org-3337	221	12	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	221	13	\Delta	\Delta	NNP
en-wikipedia-org-3337	221	14	=	=	NFP
en-wikipedia-org-3337	221	15	\Delta	\Delta	NNP
en-wikipedia-org-3337	221	16	_	_	NNP
en-wikipedia-org-3337	221	17	{	{	-LRB-
en-wikipedia-org-3337	221	18	1}\times	1}\times	CD
en-wikipedia-org-3337	221	19	\cdots	\cdots	CD
en-wikipedia-org-3337	221	20	\times	\times	CD
en-wikipedia-org-3337	221	21	\Delta	\Delta	NNP
en-wikipedia-org-3337	221	22	_	_	NNP
en-wikipedia-org-3337	221	23	{	{	-LRB-
en-wikipedia-org-3337	221	24	N	n	NN
en-wikipedia-org-3337	221	25	}	}	-RRB-
en-wikipedia-org-3337	221	26	}	}	-RRB-
en-wikipedia-org-3337	221	27	denote	denote	VB
en-wikipedia-org-3337	221	28	the	the	DT
en-wikipedia-org-3337	221	29	set	set	NN
en-wikipedia-org-3337	221	30	of	of	IN
en-wikipedia-org-3337	221	31	mixed	mix	VBN
en-wikipedia-org-3337	221	32	strategies	strategy	NNS
en-wikipedia-org-3337	221	33	for	for	IN
en-wikipedia-org-3337	221	34	the	the	DT
en-wikipedia-org-3337	221	35	players	player	NNS
en-wikipedia-org-3337	221	36	.	.	.
en-wikipedia-org-3337	222	1	The	the	DT
en-wikipedia-org-3337	222	2	finiteness	finiteness	NN
en-wikipedia-org-3337	222	3	of	of	IN
en-wikipedia-org-3337	222	4	the	the	DT
en-wikipedia-org-3337	222	5	A	a	NN
en-wikipedia-org-3337	222	6	i	i	NN
en-wikipedia-org-3337	222	7	{	{	-LRB-
en-wikipedia-org-3337	222	8	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	222	9	A_{i	a_{i	NN
en-wikipedia-org-3337	222	10	}	}	-RRB-
en-wikipedia-org-3337	222	11	}	}	-RRB-
en-wikipedia-org-3337	222	12	s	s	NN
en-wikipedia-org-3337	222	13	ensures	ensure	VBZ
en-wikipedia-org-3337	222	14	the	the	DT
en-wikipedia-org-3337	222	15	compactness	compactness	NN
en-wikipedia-org-3337	222	16	of	of	IN
en-wikipedia-org-3337	222	17	Δ	Δ	NNP
en-wikipedia-org-3337	222	18	{	{	-LRB-
en-wikipedia-org-3337	222	19	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	222	20	\Delta	\Delta	NNP
en-wikipedia-org-3337	222	21	}	}	-RRB-
en-wikipedia-org-3337	222	22	.	.	.
en-wikipedia-org-3337	223	1	We	-PRON-	PRP
en-wikipedia-org-3337	223	2	can	can	MD
en-wikipedia-org-3337	223	3	now	now	RB
en-wikipedia-org-3337	223	4	define	define	VB
en-wikipedia-org-3337	223	5	the	the	DT
en-wikipedia-org-3337	223	6	gain	gain	NN
en-wikipedia-org-3337	223	7	functions	function	NNS
en-wikipedia-org-3337	223	8	.	.	.
en-wikipedia-org-3337	224	1	For	for	IN
en-wikipedia-org-3337	224	2	a	a	DT
en-wikipedia-org-3337	224	3	mixed	mixed	JJ
en-wikipedia-org-3337	224	4	strategy	strategy	NN
en-wikipedia-org-3337	224	5	σ	σ	NN
en-wikipedia-org-3337	224	6	∈	∈	NNP
en-wikipedia-org-3337	224	7	Δ	Δ	NNP
en-wikipedia-org-3337	224	8	{	{	-LRB-
en-wikipedia-org-3337	224	9	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	224	10	\sigma	\sigma	CD
en-wikipedia-org-3337	224	11	\in	\in	NNP
en-wikipedia-org-3337	224	12	\Delta	\Delta	NNP
en-wikipedia-org-3337	224	13	}	}	-RRB-
en-wikipedia-org-3337	224	14	,	,	,
en-wikipedia-org-3337	224	15	we	-PRON-	PRP
en-wikipedia-org-3337	224	16	let	let	VBP
en-wikipedia-org-3337	224	17	the	the	DT
en-wikipedia-org-3337	224	18	gain	gain	NN
en-wikipedia-org-3337	224	19	for	for	IN
en-wikipedia-org-3337	224	20	player	player	NN
en-wikipedia-org-3337	224	21	i	i	PRP
en-wikipedia-org-3337	224	22	{	{	-LRB-
en-wikipedia-org-3337	224	23	\displaystyle	\displaystyle	UH
en-wikipedia-org-3337	224	24	i	i	NN
en-wikipedia-org-3337	224	25	}	}	-RRB-
en-wikipedia-org-3337	224	26	on	on	IN
en-wikipedia-org-3337	224	27	action	action	NN
en-wikipedia-org-3337	224	28	a	a	DT
en-wikipedia-org-3337	224	29	∈	∈	NNP
en-wikipedia-org-3337	224	30	A	a	NN
en-wikipedia-org-3337	224	31	i	i	NN
en-wikipedia-org-3337	224	32	{	{	-LRB-
en-wikipedia-org-3337	224	33	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	224	34	a\in	a\in	NNP
en-wikipedia-org-3337	224	35	A_{i	a_{i	NN
en-wikipedia-org-3337	224	36	}	}	-RRB-
en-wikipedia-org-3337	224	37	}	}	-RRB-
en-wikipedia-org-3337	224	38	be	be	VB
en-wikipedia-org-3337	224	39	Gain	gain	NN
en-wikipedia-org-3337	224	40	i	i	PRP
en-wikipedia-org-3337	224	41	(	(	-LRB-
en-wikipedia-org-3337	224	42	σ	σ	NN
en-wikipedia-org-3337	224	43	,	,	,
en-wikipedia-org-3337	224	44	a	a	LS
en-wikipedia-org-3337	224	45	)	)	-RRB-
en-wikipedia-org-3337	224	46	=	=	SYM
en-wikipedia-org-3337	224	47	max	max	NNP
en-wikipedia-org-3337	224	48	{	{	-LRB-
en-wikipedia-org-3337	224	49	0	0	NFP
en-wikipedia-org-3337	224	50	,	,	,
en-wikipedia-org-3337	224	51	u	u	NNP
en-wikipedia-org-3337	224	52	i	i	PRP
en-wikipedia-org-3337	224	53	(	(	-LRB-
en-wikipedia-org-3337	224	54	a	a	DT
en-wikipedia-org-3337	224	55	,	,	,
en-wikipedia-org-3337	224	56	σ	σ	NNP
en-wikipedia-org-3337	224	57	−	−	NNP
en-wikipedia-org-3337	224	58	i	i	PRP
en-wikipedia-org-3337	224	59	)	)	-RRB-
en-wikipedia-org-3337	224	60	−	−	NNP
en-wikipedia-org-3337	224	61	u	u	NNP
en-wikipedia-org-3337	224	62	i	i	NNP
en-wikipedia-org-3337	224	63	(	(	-LRB-
en-wikipedia-org-3337	224	64	σ	σ	NNP
en-wikipedia-org-3337	224	65	i	i	NN
en-wikipedia-org-3337	224	66	,	,	,
en-wikipedia-org-3337	224	67	σ	σ	NNP
en-wikipedia-org-3337	224	68	−	−	NNP
en-wikipedia-org-3337	224	69	i	i	PRP
en-wikipedia-org-3337	224	70	)	)	-RRB-
en-wikipedia-org-3337	224	71	}	}	-RRB-
en-wikipedia-org-3337	224	72	.	.	.
en-wikipedia-org-3337	225	1	{	{	-LRB-
en-wikipedia-org-3337	225	2	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	225	3	{	{	-LRB-
en-wikipedia-org-3337	225	4	\text{Gain}}_{i}(\sigma	\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	225	5	,	,	,
en-wikipedia-org-3337	225	6	a)=\max\{0,u_{i}(a,\sigma	a)=\max\{0,u_{i}(a,\sigma	NNP
en-wikipedia-org-3337	225	7	_	_	NNP
en-wikipedia-org-3337	225	8	{	{	-LRB-
en-wikipedia-org-3337	225	9	-i})-u_{i}(\sigma	-i})-u_{i}(\sigma	:
en-wikipedia-org-3337	225	10	_	_	NNP
en-wikipedia-org-3337	225	11	{	{	-LRB-
en-wikipedia-org-3337	225	12	i},\sigma	i},\sigma	NNP
en-wikipedia-org-3337	225	13	_	_	NNP
en-wikipedia-org-3337	225	14	{	{	-LRB-
en-wikipedia-org-3337	225	15	-i})\	-i})\	NN
en-wikipedia-org-3337	225	16	}	}	-RRB-
en-wikipedia-org-3337	225	17	.	.	.
en-wikipedia-org-3337	225	18	}	}	-RRB-
en-wikipedia-org-3337	226	1	The	the	DT
en-wikipedia-org-3337	226	2	gain	gain	NN
en-wikipedia-org-3337	226	3	function	function	NN
en-wikipedia-org-3337	226	4	represents	represent	VBZ
en-wikipedia-org-3337	226	5	the	the	DT
en-wikipedia-org-3337	226	6	benefit	benefit	NN
en-wikipedia-org-3337	226	7	a	a	DT
en-wikipedia-org-3337	226	8	player	player	NN
en-wikipedia-org-3337	226	9	gets	get	VBZ
en-wikipedia-org-3337	226	10	by	by	IN
en-wikipedia-org-3337	226	11	unilaterally	unilaterally	RB
en-wikipedia-org-3337	226	12	changing	change	VBG
en-wikipedia-org-3337	226	13	their	-PRON-	PRP$
en-wikipedia-org-3337	226	14	strategy	strategy	NN
en-wikipedia-org-3337	226	15	.	.	.
en-wikipedia-org-3337	227	1	We	-PRON-	PRP
en-wikipedia-org-3337	227	2	now	now	RB
en-wikipedia-org-3337	227	3	define	define	VBP
en-wikipedia-org-3337	227	4	g	g	NN
en-wikipedia-org-3337	227	5	=	=	NFP
en-wikipedia-org-3337	227	6	(	(	-LRB-
en-wikipedia-org-3337	227	7	g	g	NNP
en-wikipedia-org-3337	227	8	1	1	CD
en-wikipedia-org-3337	227	9	,	,	,
en-wikipedia-org-3337	227	10	…	…	NFP
en-wikipedia-org-3337	227	11	,	,	,
en-wikipedia-org-3337	227	12	g	g	NNP
en-wikipedia-org-3337	227	13	N	N	NNP
en-wikipedia-org-3337	227	14	)	)	-RRB-
en-wikipedia-org-3337	227	15	{	{	-LRB-
en-wikipedia-org-3337	227	16	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	227	17	g=(g_{1},\dotsc	g=(g_{1},\dotsc	NNS
en-wikipedia-org-3337	227	18	,	,	,
en-wikipedia-org-3337	227	19	g_{N	g_{N	NNP
en-wikipedia-org-3337	227	20	}	}	-RRB-
en-wikipedia-org-3337	227	21	)	)	-RRB-
en-wikipedia-org-3337	227	22	}	}	-RRB-
en-wikipedia-org-3337	227	23	where	where	WRB
en-wikipedia-org-3337	227	24	g	g	NNP
en-wikipedia-org-3337	227	25	i	i	NN
en-wikipedia-org-3337	227	26	(	(	-LRB-
en-wikipedia-org-3337	227	27	σ	σ	NN
en-wikipedia-org-3337	227	28	)	)	-RRB-
en-wikipedia-org-3337	227	29	(	(	-LRB-
en-wikipedia-org-3337	227	30	a	a	LS
en-wikipedia-org-3337	227	31	)	)	-RRB-
en-wikipedia-org-3337	227	32	=	=	SYM
en-wikipedia-org-3337	227	33	σ	σ	NN
en-wikipedia-org-3337	227	34	i	i	NN
en-wikipedia-org-3337	227	35	(	(	-LRB-
en-wikipedia-org-3337	227	36	a	a	LS
en-wikipedia-org-3337	227	37	)	)	-RRB-
en-wikipedia-org-3337	227	38	+	+	CD
en-wikipedia-org-3337	227	39	Gain	gain	UH
en-wikipedia-org-3337	227	40	i	i	PRP
en-wikipedia-org-3337	227	41	(	(	-LRB-
en-wikipedia-org-3337	227	42	σ	σ	NN
en-wikipedia-org-3337	227	43	,	,	,
en-wikipedia-org-3337	227	44	a	a	LS
en-wikipedia-org-3337	227	45	)	)	-RRB-
en-wikipedia-org-3337	227	46	{	{	-LRB-
en-wikipedia-org-3337	227	47	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	227	48	g_{i}(\sigma	g_{i}(\sigma	NN
en-wikipedia-org-3337	227	49	)	)	-RRB-
en-wikipedia-org-3337	227	50	(	(	-LRB-
en-wikipedia-org-3337	227	51	a)=\sigma	a)=\sigma	NNP
en-wikipedia-org-3337	227	52	_	_	NNP
en-wikipedia-org-3337	227	53	{	{	-LRB-
en-wikipedia-org-3337	227	54	i}(a)+{\text{Gain}}_{i}(\sigma	i}(a)+{\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	227	55	,	,	,
en-wikipedia-org-3337	227	56	a	a	DT
en-wikipedia-org-3337	227	57	)	)	-RRB-
en-wikipedia-org-3337	227	58	}	}	-RRB-
en-wikipedia-org-3337	227	59	for	for	IN
en-wikipedia-org-3337	227	60	σ	σ	NNP
en-wikipedia-org-3337	227	61	∈	∈	NNP
en-wikipedia-org-3337	227	62	Δ	Δ	NNP
en-wikipedia-org-3337	227	63	,	,	,
en-wikipedia-org-3337	227	64	a	a	DT
en-wikipedia-org-3337	227	65	∈	∈	NNP
en-wikipedia-org-3337	227	66	A	a	NN
en-wikipedia-org-3337	227	67	i	i	NN
en-wikipedia-org-3337	227	68	{	{	-LRB-
en-wikipedia-org-3337	227	69	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	227	70	\sigma	\sigma	CD
en-wikipedia-org-3337	227	71	\in	\in	NNP
en-wikipedia-org-3337	227	72	\Delta	\Delta	NNP
en-wikipedia-org-3337	227	73	,	,	,
en-wikipedia-org-3337	227	74	a\in	a\in	NNP
en-wikipedia-org-3337	227	75	A_{i	A_{i	NNP
en-wikipedia-org-3337	227	76	}	}	-RRB-
en-wikipedia-org-3337	227	77	}	}	-RRB-
en-wikipedia-org-3337	227	78	.	.	.
en-wikipedia-org-3337	228	1	We	-PRON-	PRP
en-wikipedia-org-3337	228	2	see	see	VBP
en-wikipedia-org-3337	228	3	that	that	IN
en-wikipedia-org-3337	228	4	∑	∑	.
en-wikipedia-org-3337	228	5	a	a	DT
en-wikipedia-org-3337	228	6	∈	∈	NNP
en-wikipedia-org-3337	228	7	A	a	NN
en-wikipedia-org-3337	228	8	i	i	NN
en-wikipedia-org-3337	228	9	g	g	NN
en-wikipedia-org-3337	228	10	i	i	PRP
en-wikipedia-org-3337	228	11	(	(	-LRB-
en-wikipedia-org-3337	228	12	σ	σ	NN
en-wikipedia-org-3337	228	13	)	)	-RRB-
en-wikipedia-org-3337	228	14	(	(	-LRB-
en-wikipedia-org-3337	228	15	a	a	LS
en-wikipedia-org-3337	228	16	)	)	-RRB-
en-wikipedia-org-3337	228	17	=	=	NFP
en-wikipedia-org-3337	228	18	∑	∑	.
en-wikipedia-org-3337	228	19	a	a	DT
en-wikipedia-org-3337	228	20	∈	∈	NNP
en-wikipedia-org-3337	228	21	A	a	NN
en-wikipedia-org-3337	228	22	i	i	NN
en-wikipedia-org-3337	228	23	σ	σ	XX
en-wikipedia-org-3337	228	24	i	i	PRP
en-wikipedia-org-3337	228	25	(	(	-LRB-
en-wikipedia-org-3337	228	26	a	a	LS
en-wikipedia-org-3337	228	27	)	)	-RRB-
en-wikipedia-org-3337	228	28	+	+	CD
en-wikipedia-org-3337	228	29	Gain	gain	UH
en-wikipedia-org-3337	228	30	i	i	PRP
en-wikipedia-org-3337	228	31	(	(	-LRB-
en-wikipedia-org-3337	228	32	σ	σ	NN
en-wikipedia-org-3337	228	33	,	,	,
en-wikipedia-org-3337	228	34	a	a	NN
en-wikipedia-org-3337	228	35	)	)	-RRB-
en-wikipedia-org-3337	228	36	=	=	SYM
en-wikipedia-org-3337	228	37	1	1	CD
en-wikipedia-org-3337	228	38	+	+	SYM
en-wikipedia-org-3337	228	39	∑	∑	CD
en-wikipedia-org-3337	228	40	a	a	DT
en-wikipedia-org-3337	228	41	∈	∈	NNP
en-wikipedia-org-3337	228	42	A	A	NNP
en-wikipedia-org-3337	228	43	i	i	NN
en-wikipedia-org-3337	228	44	Gain	gain	VBP
en-wikipedia-org-3337	228	45	i	i	PRP
en-wikipedia-org-3337	228	46	(	(	-LRB-
en-wikipedia-org-3337	228	47	σ	σ	NN
en-wikipedia-org-3337	228	48	,	,	,
en-wikipedia-org-3337	228	49	a	a	LS
en-wikipedia-org-3337	228	50	)	)	-RRB-
en-wikipedia-org-3337	228	51	>	>	XX
en-wikipedia-org-3337	228	52	0	0	CD
en-wikipedia-org-3337	228	53	.	.	.
en-wikipedia-org-3337	229	1	{	{	-LRB-
en-wikipedia-org-3337	229	2	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	229	3	\sum	\sum	CD
en-wikipedia-org-3337	229	4	_	_	NNP
en-wikipedia-org-3337	229	5	{	{	-LRB-
en-wikipedia-org-3337	229	6	a\in	a\in	NNP
en-wikipedia-org-3337	229	7	A_{i}}g_{i}(\sigma	A_{i}}g_{i}(\sigma	NNP
en-wikipedia-org-3337	229	8	)	)	-RRB-
en-wikipedia-org-3337	229	9	(	(	-LRB-
en-wikipedia-org-3337	229	10	a)=\sum	a)=\sum	NNP
en-wikipedia-org-3337	229	11	_	_	NNP
en-wikipedia-org-3337	229	12	{	{	-LRB-
en-wikipedia-org-3337	229	13	a\in	a\in	NNP
en-wikipedia-org-3337	229	14	A_{i}}\sigma	A_{i}}\sigma	NNP
en-wikipedia-org-3337	229	15	_	_	NNP
en-wikipedia-org-3337	229	16	{	{	-LRB-
en-wikipedia-org-3337	229	17	i}(a)+{\text{Gain}}_{i}(\sigma	i}(a)+{\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	229	18	,	,	,
en-wikipedia-org-3337	229	19	a)=1+\sum	a)=1+\sum	NNP
en-wikipedia-org-3337	229	20	_	_	NNP
en-wikipedia-org-3337	229	21	{	{	-LRB-
en-wikipedia-org-3337	229	22	a\in	a\in	NNP
en-wikipedia-org-3337	229	23	A_{i}}{\text{Gain}}_{i}(\sigma	A_{i}}{\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	229	24	,	,	,
en-wikipedia-org-3337	229	25	a)>0	a)>0	:
en-wikipedia-org-3337	229	26	.	.	.
en-wikipedia-org-3337	229	27	}	}	-RRB-
en-wikipedia-org-3337	230	1	Next	next	RB
en-wikipedia-org-3337	230	2	we	-PRON-	PRP
en-wikipedia-org-3337	230	3	define	define	VBP
en-wikipedia-org-3337	230	4	:	:	:
en-wikipedia-org-3337	230	5	{	{	-LRB-
en-wikipedia-org-3337	230	6	f	f	NNP
en-wikipedia-org-3337	230	7	=	=	NFP
en-wikipedia-org-3337	230	8	(	(	-LRB-
en-wikipedia-org-3337	230	9	f	f	NNP
en-wikipedia-org-3337	230	10	1	1	CD
en-wikipedia-org-3337	230	11	,	,	,
en-wikipedia-org-3337	230	12	⋯	⋯	NNP
en-wikipedia-org-3337	230	13	,	,	,
en-wikipedia-org-3337	230	14	f	f	NNP
en-wikipedia-org-3337	230	15	N	N	NNP
en-wikipedia-org-3337	230	16	)	)	-RRB-
en-wikipedia-org-3337	230	17	:	:	:
en-wikipedia-org-3337	230	18	Δ	δ	NN
en-wikipedia-org-3337	230	19	→	→	IN
en-wikipedia-org-3337	230	20	Δ	Δ	NNP
en-wikipedia-org-3337	230	21	f	f	NNP
en-wikipedia-org-3337	230	22	i	i	NN
en-wikipedia-org-3337	230	23	(	(	-LRB-
en-wikipedia-org-3337	230	24	σ	σ	NN
en-wikipedia-org-3337	230	25	)	)	-RRB-
en-wikipedia-org-3337	230	26	(	(	-LRB-
en-wikipedia-org-3337	230	27	a	a	LS
en-wikipedia-org-3337	230	28	)	)	-RRB-
en-wikipedia-org-3337	230	29	=	=	NFP
en-wikipedia-org-3337	230	30	g	g	NN
en-wikipedia-org-3337	230	31	i	i	NN
en-wikipedia-org-3337	230	32	(	(	-LRB-
en-wikipedia-org-3337	230	33	σ	σ	NN
en-wikipedia-org-3337	230	34	)	)	-RRB-
en-wikipedia-org-3337	230	35	(	(	-LRB-
en-wikipedia-org-3337	230	36	a	a	DT
en-wikipedia-org-3337	230	37	)	)	-RRB-
en-wikipedia-org-3337	230	38	∑	∑	.
en-wikipedia-org-3337	230	39	b	b	NN
en-wikipedia-org-3337	230	40	∈	∈	NNP
en-wikipedia-org-3337	230	41	A	A	NNP
en-wikipedia-org-3337	230	42	i	i	NN
en-wikipedia-org-3337	230	43	g	g	NN
en-wikipedia-org-3337	230	44	i	i	PRP
en-wikipedia-org-3337	230	45	(	(	-LRB-
en-wikipedia-org-3337	230	46	σ	σ	NN
en-wikipedia-org-3337	230	47	)	)	-RRB-
en-wikipedia-org-3337	230	48	(	(	-LRB-
en-wikipedia-org-3337	230	49	b	b	NN
en-wikipedia-org-3337	230	50	)	)	-RRB-
en-wikipedia-org-3337	230	51	a	a	LS
en-wikipedia-org-3337	230	52	∈	∈	NNP
en-wikipedia-org-3337	230	53	A	a	NN
en-wikipedia-org-3337	230	54	i	i	PRP
en-wikipedia-org-3337	230	55	{	{	-LRB-
en-wikipedia-org-3337	230	56	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	230	57	{	{	-LRB-
en-wikipedia-org-3337	230	58	\begin{cases}f=(f_{1},\cdots	\begin{cases}f=(f_{1},\cdots	UH
en-wikipedia-org-3337	230	59	,	,	,
en-wikipedia-org-3337	230	60	f_{N}):\Delta	f_{N}):\Delta	.
en-wikipedia-org-3337	230	61	\to	\to	NNP
en-wikipedia-org-3337	230	62	\Delta	\Delta	NNP
en-wikipedia-org-3337	230	63	\\f_{i}(\sigma	\\f_{i}(\sigma	NN
en-wikipedia-org-3337	230	64	)	)	-RRB-
en-wikipedia-org-3337	230	65	(	(	-LRB-
en-wikipedia-org-3337	230	66	a)={\frac	a)={\frac	NFP
en-wikipedia-org-3337	230	67	{	{	-LRB-
en-wikipedia-org-3337	230	68	g_{i}(\sigma	g_{i}(\sigma	NN
en-wikipedia-org-3337	230	69	)	)	-RRB-
en-wikipedia-org-3337	230	70	(	(	-LRB-
en-wikipedia-org-3337	230	71	a)}{\sum	a)}{\sum	NNP
en-wikipedia-org-3337	230	72	_	_	NNP
en-wikipedia-org-3337	230	73	{	{	-LRB-
en-wikipedia-org-3337	230	74	b\in	b\in	NNP
en-wikipedia-org-3337	230	75	A_{i}}g_{i}(\sigma	A_{i}}g_{i}(\sigma	NNP
en-wikipedia-org-3337	230	76	)	)	-RRB-
en-wikipedia-org-3337	230	77	(	(	-LRB-
en-wikipedia-org-3337	230	78	b)}}&a\in	b)}}&a\in	NNP
en-wikipedia-org-3337	230	79	A_{i}\end{cases	A_{i}\end{cases	NNP
en-wikipedia-org-3337	230	80	}	}	-RRB-
en-wikipedia-org-3337	230	81	}	}	-RRB-
en-wikipedia-org-3337	230	82	}	}	-RRB-
en-wikipedia-org-3337	230	83	It	-PRON-	PRP
en-wikipedia-org-3337	230	84	is	be	VBZ
en-wikipedia-org-3337	230	85	easy	easy	JJ
en-wikipedia-org-3337	230	86	to	to	TO
en-wikipedia-org-3337	230	87	see	see	VB
en-wikipedia-org-3337	230	88	that	that	IN
en-wikipedia-org-3337	230	89	each	each	DT
en-wikipedia-org-3337	230	90	f	f	XX
en-wikipedia-org-3337	230	91	i	i	PRP
en-wikipedia-org-3337	230	92	{	{	-LRB-
en-wikipedia-org-3337	230	93	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	230	94	f_{i	f_{i	NN
en-wikipedia-org-3337	230	95	}	}	-RRB-
en-wikipedia-org-3337	230	96	}	}	-RRB-
en-wikipedia-org-3337	230	97	is	be	VBZ
en-wikipedia-org-3337	230	98	a	a	DT
en-wikipedia-org-3337	230	99	valid	valid	JJ
en-wikipedia-org-3337	230	100	mixed	mixed	JJ
en-wikipedia-org-3337	230	101	strategy	strategy	NN
en-wikipedia-org-3337	230	102	in	in	IN
en-wikipedia-org-3337	230	103	Δ	Δ	NNP
en-wikipedia-org-3337	230	104	i	i	PRP
en-wikipedia-org-3337	230	105	{	{	-LRB-
en-wikipedia-org-3337	230	106	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	230	107	\Delta	\Delta	NNP
en-wikipedia-org-3337	230	108	_	_	NNP
en-wikipedia-org-3337	230	109	{	{	-LRB-
en-wikipedia-org-3337	230	110	i	i	NN
en-wikipedia-org-3337	230	111	}	}	-RRB-
en-wikipedia-org-3337	230	112	}	}	-RRB-
en-wikipedia-org-3337	230	113	.	.	.
en-wikipedia-org-3337	231	1	It	-PRON-	PRP
en-wikipedia-org-3337	231	2	is	be	VBZ
en-wikipedia-org-3337	231	3	also	also	RB
en-wikipedia-org-3337	231	4	easy	easy	JJ
en-wikipedia-org-3337	231	5	to	to	TO
en-wikipedia-org-3337	231	6	check	check	VB
en-wikipedia-org-3337	231	7	that	that	IN
en-wikipedia-org-3337	231	8	each	each	DT
en-wikipedia-org-3337	231	9	f	f	XX
en-wikipedia-org-3337	231	10	i	i	PRP
en-wikipedia-org-3337	231	11	{	{	-LRB-
en-wikipedia-org-3337	231	12	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	231	13	f_{i	f_{i	NN
en-wikipedia-org-3337	231	14	}	}	-RRB-
en-wikipedia-org-3337	231	15	}	}	-RRB-
en-wikipedia-org-3337	231	16	is	be	VBZ
en-wikipedia-org-3337	231	17	a	a	DT
en-wikipedia-org-3337	231	18	continuous	continuous	JJ
en-wikipedia-org-3337	231	19	function	function	NN
en-wikipedia-org-3337	231	20	of	of	IN
en-wikipedia-org-3337	231	21	σ	σ	NN
en-wikipedia-org-3337	231	22	{	{	-LRB-
en-wikipedia-org-3337	231	23	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	231	24	\sigma	\sigma	CD
en-wikipedia-org-3337	231	25	}	}	-RRB-
en-wikipedia-org-3337	231	26	,	,	,
en-wikipedia-org-3337	231	27	and	and	CC
en-wikipedia-org-3337	231	28	hence	hence	RB
en-wikipedia-org-3337	231	29	f	f	NNP
en-wikipedia-org-3337	231	30	{	{	-LRB-
en-wikipedia-org-3337	231	31	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	231	32	f	f	NN
en-wikipedia-org-3337	231	33	}	}	-RRB-
en-wikipedia-org-3337	231	34	is	be	VBZ
en-wikipedia-org-3337	231	35	a	a	DT
en-wikipedia-org-3337	231	36	continuous	continuous	JJ
en-wikipedia-org-3337	231	37	function	function	NN
en-wikipedia-org-3337	231	38	.	.	.
en-wikipedia-org-3337	232	1	As	as	IN
en-wikipedia-org-3337	232	2	the	the	DT
en-wikipedia-org-3337	232	3	cross	cross	NN
en-wikipedia-org-3337	232	4	product	product	NN
en-wikipedia-org-3337	232	5	of	of	IN
en-wikipedia-org-3337	232	6	a	a	DT
en-wikipedia-org-3337	232	7	finite	finite	JJ
en-wikipedia-org-3337	232	8	number	number	NN
en-wikipedia-org-3337	232	9	of	of	IN
en-wikipedia-org-3337	232	10	compact	compact	JJ
en-wikipedia-org-3337	232	11	convex	convex	NNP
en-wikipedia-org-3337	232	12	sets	set	NNS
en-wikipedia-org-3337	232	13	,	,	,
en-wikipedia-org-3337	232	14	Δ	Δ	NNP
en-wikipedia-org-3337	232	15	{	{	-LRB-
en-wikipedia-org-3337	232	16	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	232	17	\Delta	\Delta	NNP
en-wikipedia-org-3337	232	18	}	}	-RRB-
en-wikipedia-org-3337	232	19	is	be	VBZ
en-wikipedia-org-3337	232	20	also	also	RB
en-wikipedia-org-3337	232	21	compact	compact	JJ
en-wikipedia-org-3337	232	22	and	and	CC
en-wikipedia-org-3337	232	23	convex	convex	NNS
en-wikipedia-org-3337	232	24	.	.	.
en-wikipedia-org-3337	233	1	Applying	apply	VBG
en-wikipedia-org-3337	233	2	the	the	DT
en-wikipedia-org-3337	233	3	Brouwer	Brouwer	NNP
en-wikipedia-org-3337	233	4	fixed	fix	VBN
en-wikipedia-org-3337	233	5	point	point	NN
en-wikipedia-org-3337	233	6	theorem	theorem	RB
en-wikipedia-org-3337	233	7	to	to	IN
en-wikipedia-org-3337	233	8	f	f	NNP
en-wikipedia-org-3337	233	9	{	{	-LRB-
en-wikipedia-org-3337	233	10	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	233	11	f	f	NNP
en-wikipedia-org-3337	233	12	}	}	-RRB-
en-wikipedia-org-3337	233	13	and	and	CC
en-wikipedia-org-3337	233	14	Δ	Δ	NNP
en-wikipedia-org-3337	233	15	{	{	-LRB-
en-wikipedia-org-3337	233	16	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	233	17	\Delta	\Delta	NNP
en-wikipedia-org-3337	233	18	}	}	-RRB-
en-wikipedia-org-3337	233	19	we	-PRON-	PRP
en-wikipedia-org-3337	233	20	conclude	conclude	VBP
en-wikipedia-org-3337	233	21	that	that	IN
en-wikipedia-org-3337	233	22	f	f	NN
en-wikipedia-org-3337	233	23	{	{	-LRB-
en-wikipedia-org-3337	233	24	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	233	25	f	f	NN
en-wikipedia-org-3337	233	26	}	}	-RRB-
en-wikipedia-org-3337	233	27	has	have	VBZ
en-wikipedia-org-3337	233	28	a	a	DT
en-wikipedia-org-3337	233	29	fixed	fix	VBN
en-wikipedia-org-3337	233	30	point	point	NN
en-wikipedia-org-3337	233	31	in	in	IN
en-wikipedia-org-3337	233	32	Δ	Δ	NNP
en-wikipedia-org-3337	233	33	{	{	-LRB-
en-wikipedia-org-3337	233	34	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	233	35	\Delta	\Delta	NNP
en-wikipedia-org-3337	233	36	}	}	-RRB-
en-wikipedia-org-3337	233	37	,	,	,
en-wikipedia-org-3337	233	38	call	call	VB
en-wikipedia-org-3337	233	39	it	-PRON-	PRP
en-wikipedia-org-3337	233	40	σ	σ	XX
en-wikipedia-org-3337	233	41	∗	∗	NNP
en-wikipedia-org-3337	233	42	{	{	-LRB-
en-wikipedia-org-3337	233	43	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	233	44	\sigma	\sigma	CD
en-wikipedia-org-3337	233	45	^	^	NN
en-wikipedia-org-3337	233	46	{	{	-LRB-
en-wikipedia-org-3337	233	47	*	*	NFP
en-wikipedia-org-3337	233	48	}	}	-RRB-
en-wikipedia-org-3337	233	49	}	}	-RRB-
en-wikipedia-org-3337	233	50	.	.	.
en-wikipedia-org-3337	234	1	We	-PRON-	PRP
en-wikipedia-org-3337	234	2	claim	claim	VBP
en-wikipedia-org-3337	234	3	that	that	IN
en-wikipedia-org-3337	234	4	σ	σ	NNP
en-wikipedia-org-3337	234	5	∗	∗	NNP
en-wikipedia-org-3337	234	6	{	{	-LRB-
en-wikipedia-org-3337	234	7	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	234	8	\sigma	\sigma	CD
en-wikipedia-org-3337	234	9	^	^	NN
en-wikipedia-org-3337	234	10	{	{	-LRB-
en-wikipedia-org-3337	234	11	*	*	NFP
en-wikipedia-org-3337	234	12	}	}	-RRB-
en-wikipedia-org-3337	234	13	}	}	-RRB-
en-wikipedia-org-3337	234	14	is	be	VBZ
en-wikipedia-org-3337	234	15	a	a	DT
en-wikipedia-org-3337	234	16	Nash	Nash	NNP
en-wikipedia-org-3337	234	17	equilibrium	equilibrium	NN
en-wikipedia-org-3337	234	18	in	in	IN
en-wikipedia-org-3337	234	19	G	g	NN
en-wikipedia-org-3337	234	20	{	{	-LRB-
en-wikipedia-org-3337	234	21	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	234	22	G	g	NN
en-wikipedia-org-3337	234	23	}	}	-RRB-
en-wikipedia-org-3337	234	24	.	.	.
en-wikipedia-org-3337	235	1	For	for	IN
en-wikipedia-org-3337	235	2	this	this	DT
en-wikipedia-org-3337	235	3	purpose	purpose	NN
en-wikipedia-org-3337	235	4	,	,	,
en-wikipedia-org-3337	235	5	it	-PRON-	PRP
en-wikipedia-org-3337	235	6	suffices	suffice	VBZ
en-wikipedia-org-3337	235	7	to	to	TO
en-wikipedia-org-3337	235	8	show	show	VB
en-wikipedia-org-3337	235	9	that	that	IN
en-wikipedia-org-3337	235	10	∀	∀	NNP
en-wikipedia-org-3337	235	11	i	i	PRP
en-wikipedia-org-3337	235	12	∈	∈	VBP
en-wikipedia-org-3337	235	13	{	{	-LRB-
en-wikipedia-org-3337	235	14	1	1	CD
en-wikipedia-org-3337	235	15	,	,	,
en-wikipedia-org-3337	235	16	⋯	⋯	NNP
en-wikipedia-org-3337	235	17	,	,	,
en-wikipedia-org-3337	235	18	N	N	NNP
en-wikipedia-org-3337	235	19	}	}	-RRB-
en-wikipedia-org-3337	235	20	,	,	,
en-wikipedia-org-3337	235	21	∀	∀	NNP
en-wikipedia-org-3337	235	22	a	a	DT
en-wikipedia-org-3337	235	23	∈	∈	NNP
en-wikipedia-org-3337	235	24	A	a	NN
en-wikipedia-org-3337	235	25	i	i	PRP
en-wikipedia-org-3337	235	26	:	:	:
en-wikipedia-org-3337	235	27	Gain	gain	VB
en-wikipedia-org-3337	235	28	i	i	PRP
en-wikipedia-org-3337	235	29	(	(	-LRB-
en-wikipedia-org-3337	235	30	σ	σ	NNP
en-wikipedia-org-3337	235	31	∗	∗	NNP
en-wikipedia-org-3337	235	32	,	,	,
en-wikipedia-org-3337	235	33	a	a	LS
en-wikipedia-org-3337	235	34	)	)	-RRB-
en-wikipedia-org-3337	235	35	=	=	SYM
en-wikipedia-org-3337	235	36	0	0	NFP
en-wikipedia-org-3337	235	37	.	.	.
en-wikipedia-org-3337	236	1	{	{	-LRB-
en-wikipedia-org-3337	236	2	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	236	3	\forall	\forall	CD
en-wikipedia-org-3337	236	4	i\in	i\in	NNP
en-wikipedia-org-3337	236	5	\{1,\cdots	\{1,\cdots	NNPS
en-wikipedia-org-3337	236	6	,	,	,
en-wikipedia-org-3337	236	7	N\},\forall	N\},\forall	NNP
en-wikipedia-org-3337	236	8	a\in	a\in	NNP
en-wikipedia-org-3337	236	9	A_{i}:\quad	A_{i}:\quad	NNPS
en-wikipedia-org-3337	236	10	{	{	-LRB-
en-wikipedia-org-3337	236	11	\text{Gain}}_{i}(\sigma	\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	236	12	^{*},a)=0	^{*},a)=0	NN
en-wikipedia-org-3337	236	13	.	.	.
en-wikipedia-org-3337	236	14	}	}	-RRB-
en-wikipedia-org-3337	237	1	This	this	DT
en-wikipedia-org-3337	237	2	simply	simply	RB
en-wikipedia-org-3337	237	3	states	state	VBZ
en-wikipedia-org-3337	237	4	that	that	IN
en-wikipedia-org-3337	237	5	each	each	DT
en-wikipedia-org-3337	237	6	player	player	NN
en-wikipedia-org-3337	237	7	gains	gain	VBZ
en-wikipedia-org-3337	237	8	no	no	DT
en-wikipedia-org-3337	237	9	benefit	benefit	NN
en-wikipedia-org-3337	237	10	by	by	IN
en-wikipedia-org-3337	237	11	unilaterally	unilaterally	RB
en-wikipedia-org-3337	237	12	changing	change	VBG
en-wikipedia-org-3337	237	13	their	-PRON-	PRP$
en-wikipedia-org-3337	237	14	strategy	strategy	NN
en-wikipedia-org-3337	237	15	,	,	,
en-wikipedia-org-3337	237	16	which	which	WDT
en-wikipedia-org-3337	237	17	is	be	VBZ
en-wikipedia-org-3337	237	18	exactly	exactly	RB
en-wikipedia-org-3337	237	19	the	the	DT
en-wikipedia-org-3337	237	20	necessary	necessary	JJ
en-wikipedia-org-3337	237	21	condition	condition	NN
en-wikipedia-org-3337	237	22	for	for	IN
en-wikipedia-org-3337	237	23	a	a	DT
en-wikipedia-org-3337	237	24	Nash	Nash	NNP
en-wikipedia-org-3337	237	25	equilibrium	equilibrium	NN
en-wikipedia-org-3337	237	26	.	.	.
en-wikipedia-org-3337	238	1	Now	now	RB
en-wikipedia-org-3337	238	2	assume	assume	VB
en-wikipedia-org-3337	238	3	that	that	IN
en-wikipedia-org-3337	238	4	the	the	DT
en-wikipedia-org-3337	238	5	gains	gain	NNS
en-wikipedia-org-3337	238	6	are	be	VBP
en-wikipedia-org-3337	238	7	not	not	RB
en-wikipedia-org-3337	238	8	all	all	DT
en-wikipedia-org-3337	238	9	zero	zero	CD
en-wikipedia-org-3337	238	10	.	.	.
en-wikipedia-org-3337	239	1	Therefore	therefore	RB
en-wikipedia-org-3337	239	2	,	,	,
en-wikipedia-org-3337	239	3	∃	∃	JJ
en-wikipedia-org-3337	239	4	i	i	PRP
en-wikipedia-org-3337	239	5	∈	∈	VBD
en-wikipedia-org-3337	239	6	{	{	-LRB-
en-wikipedia-org-3337	239	7	1	1	CD
en-wikipedia-org-3337	239	8	,	,	,
en-wikipedia-org-3337	239	9	⋯	⋯	NNP
en-wikipedia-org-3337	239	10	,	,	,
en-wikipedia-org-3337	239	11	N	N	NNP
en-wikipedia-org-3337	239	12	}	}	-RRB-
en-wikipedia-org-3337	239	13	,	,	,
en-wikipedia-org-3337	239	14	{	{	-LRB-
en-wikipedia-org-3337	239	15	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	239	16	\exists	\exists	CD
en-wikipedia-org-3337	239	17	i\in	i\in	NN
en-wikipedia-org-3337	239	18	\{1,\cdots	\{1,\cdots	NNPS
en-wikipedia-org-3337	239	19	,	,	,
en-wikipedia-org-3337	239	20	N\	N\	NNP
en-wikipedia-org-3337	239	21	}	}	-RRB-
en-wikipedia-org-3337	239	22	,	,	,
en-wikipedia-org-3337	239	23	}	}	-RRB-
en-wikipedia-org-3337	239	24	and	and	CC
en-wikipedia-org-3337	239	25	a	a	DT
en-wikipedia-org-3337	239	26	∈	∈	NNP
en-wikipedia-org-3337	239	27	A	a	NN
en-wikipedia-org-3337	239	28	i	i	NN
en-wikipedia-org-3337	239	29	{	{	-LRB-
en-wikipedia-org-3337	239	30	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	239	31	a\in	a\in	NNP
en-wikipedia-org-3337	239	32	A_{i	A_{i	NNP
en-wikipedia-org-3337	239	33	}	}	-RRB-
en-wikipedia-org-3337	239	34	}	}	-RRB-
en-wikipedia-org-3337	239	35	such	such	JJ
en-wikipedia-org-3337	239	36	that	that	IN
en-wikipedia-org-3337	239	37	Gain	Gain	NNP
en-wikipedia-org-3337	239	38	i	i	PRP
en-wikipedia-org-3337	239	39	(	(	-LRB-
en-wikipedia-org-3337	239	40	σ	σ	NNP
en-wikipedia-org-3337	239	41	∗	∗	NNP
en-wikipedia-org-3337	239	42	,	,	,
en-wikipedia-org-3337	239	43	a	a	LS
en-wikipedia-org-3337	239	44	)	)	-RRB-
en-wikipedia-org-3337	239	45	>	>	XX
en-wikipedia-org-3337	239	46	0	0	NFP
en-wikipedia-org-3337	239	47	{	{	-LRB-
en-wikipedia-org-3337	239	48	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	239	49	{	{	-LRB-
en-wikipedia-org-3337	239	50	\text{Gain}}_{i}(\sigma	\text{gain}}_{i}(\sigma	CD
en-wikipedia-org-3337	239	51	^{*},a)>0	^{*},a)>0	NFP
en-wikipedia-org-3337	239	52	}	}	-RRB-
en-wikipedia-org-3337	239	53	.	.	.
en-wikipedia-org-3337	240	1	Note	note	VB
en-wikipedia-org-3337	240	2	then	then	RB
en-wikipedia-org-3337	240	3	that	that	DT
en-wikipedia-org-3337	240	4	∑	∑	.
en-wikipedia-org-3337	240	5	a	a	DT
en-wikipedia-org-3337	240	6	∈	∈	NNP
en-wikipedia-org-3337	240	7	A	a	NN
en-wikipedia-org-3337	240	8	i	i	NN
en-wikipedia-org-3337	240	9	g	g	NN
en-wikipedia-org-3337	240	10	i	i	PRP
en-wikipedia-org-3337	240	11	(	(	-LRB-
en-wikipedia-org-3337	240	12	σ	σ	NNP
en-wikipedia-org-3337	240	13	∗	∗	NNP
en-wikipedia-org-3337	240	14	,	,	,
en-wikipedia-org-3337	240	15	a	a	LS
en-wikipedia-org-3337	240	16	)	)	-RRB-
en-wikipedia-org-3337	240	17	=	=	SYM
en-wikipedia-org-3337	240	18	1	1	CD
en-wikipedia-org-3337	240	19	+	+	SYM
en-wikipedia-org-3337	240	20	∑	∑	CD
en-wikipedia-org-3337	240	21	a	a	DT
en-wikipedia-org-3337	240	22	∈	∈	NNP
en-wikipedia-org-3337	240	23	A	A	NNP
en-wikipedia-org-3337	240	24	i	i	NN
en-wikipedia-org-3337	240	25	Gain	gain	VBP
en-wikipedia-org-3337	240	26	i	i	PRP
en-wikipedia-org-3337	240	27	(	(	-LRB-
en-wikipedia-org-3337	240	28	σ	σ	NNP
en-wikipedia-org-3337	240	29	∗	∗	NNP
en-wikipedia-org-3337	240	30	,	,	,
en-wikipedia-org-3337	240	31	a	a	LS
en-wikipedia-org-3337	240	32	)	)	-RRB-
en-wikipedia-org-3337	240	33	>	>	XX
en-wikipedia-org-3337	240	34	1	1	CD
en-wikipedia-org-3337	240	35	.	.	.
en-wikipedia-org-3337	241	1	{	{	-LRB-
en-wikipedia-org-3337	241	2	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	241	3	\sum	\sum	CD
en-wikipedia-org-3337	241	4	_	_	NNP
en-wikipedia-org-3337	241	5	{	{	-LRB-
en-wikipedia-org-3337	241	6	a\in	a\in	NNP
en-wikipedia-org-3337	241	7	A_{i}}g_{i}(\sigma	A_{i}}g_{i}(\sigma	NNP
en-wikipedia-org-3337	241	8	^{*},a)=1+\sum	^{*},a)=1+\sum	NFP
en-wikipedia-org-3337	241	9	_	_	NNP
en-wikipedia-org-3337	241	10	{	{	-LRB-
en-wikipedia-org-3337	241	11	a\in	a\in	NNP
en-wikipedia-org-3337	241	12	A_{i}}{\text{Gain}}_{i}(\sigma	A_{i}}{\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	241	13	^{*},a)>1	^{*},a)>1	NFP
en-wikipedia-org-3337	241	14	.	.	.
en-wikipedia-org-3337	241	15	}	}	-RRB-
en-wikipedia-org-3337	242	1	So	so	RB
en-wikipedia-org-3337	242	2	let	let	VB
en-wikipedia-org-3337	242	3	C	C	NNP
en-wikipedia-org-3337	242	4	=	=	NFP
en-wikipedia-org-3337	242	5	∑	∑	.
en-wikipedia-org-3337	242	6	a	a	DT
en-wikipedia-org-3337	242	7	∈	∈	NNP
en-wikipedia-org-3337	242	8	A	a	NN
en-wikipedia-org-3337	242	9	i	i	NN
en-wikipedia-org-3337	242	10	g	g	NN
en-wikipedia-org-3337	242	11	i	i	PRP
en-wikipedia-org-3337	242	12	(	(	-LRB-
en-wikipedia-org-3337	242	13	σ	σ	NNP
en-wikipedia-org-3337	242	14	∗	∗	NNP
en-wikipedia-org-3337	242	15	,	,	,
en-wikipedia-org-3337	242	16	a	a	DT
en-wikipedia-org-3337	242	17	)	)	-RRB-
en-wikipedia-org-3337	242	18	.	.	.
en-wikipedia-org-3337	243	1	{	{	-LRB-
en-wikipedia-org-3337	243	2	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	243	3	C=\sum	c=\sum	NN
en-wikipedia-org-3337	243	4	_	_	NNP
en-wikipedia-org-3337	243	5	{	{	-LRB-
en-wikipedia-org-3337	243	6	a\in	a\in	NNP
en-wikipedia-org-3337	243	7	A_{i}}g_{i}(\sigma	A_{i}}g_{i}(\sigma	NNP
en-wikipedia-org-3337	243	8	^{*},a	^{*},a	.
en-wikipedia-org-3337	243	9	)	)	-RRB-
en-wikipedia-org-3337	243	10	.	.	.
en-wikipedia-org-3337	243	11	}	}	-RRB-
en-wikipedia-org-3337	244	1	Also	also	RB
en-wikipedia-org-3337	244	2	we	-PRON-	PRP
en-wikipedia-org-3337	244	3	shall	shall	MD
en-wikipedia-org-3337	244	4	denote	denote	VB
en-wikipedia-org-3337	244	5	Gain	Gain	NNP
en-wikipedia-org-3337	244	6	(	(	-LRB-
en-wikipedia-org-3337	244	7	i	i	PRP
en-wikipedia-org-3337	244	8	,	,	,
en-wikipedia-org-3337	244	9	⋅	⋅	NNP
en-wikipedia-org-3337	244	10	)	)	-RRB-
en-wikipedia-org-3337	244	11	{	{	-LRB-
en-wikipedia-org-3337	244	12	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	244	13	{	{	-LRB-
en-wikipedia-org-3337	244	14	\text{Gain}}(i,\cdot	\text{gain}}(i,\cdot	CD
en-wikipedia-org-3337	244	15	)	)	-RRB-
en-wikipedia-org-3337	244	16	}	}	-RRB-
en-wikipedia-org-3337	244	17	as	as	IN
en-wikipedia-org-3337	244	18	the	the	DT
en-wikipedia-org-3337	244	19	gain	gain	NN
en-wikipedia-org-3337	244	20	vector	vector	NN
en-wikipedia-org-3337	244	21	indexed	index	VBN
en-wikipedia-org-3337	244	22	by	by	IN
en-wikipedia-org-3337	244	23	actions	action	NNS
en-wikipedia-org-3337	244	24	in	in	IN
en-wikipedia-org-3337	244	25	A	a	DT
en-wikipedia-org-3337	244	26	i	i	NN
en-wikipedia-org-3337	244	27	{	{	-LRB-
en-wikipedia-org-3337	244	28	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	244	29	A_{i	a_{i	NN
en-wikipedia-org-3337	244	30	}	}	-RRB-
en-wikipedia-org-3337	244	31	}	}	-RRB-
en-wikipedia-org-3337	244	32	.	.	.
en-wikipedia-org-3337	245	1	Since	since	IN
en-wikipedia-org-3337	245	2	σ	σ	NNP
en-wikipedia-org-3337	245	3	∗	∗	NNP
en-wikipedia-org-3337	245	4	{	{	-LRB-
en-wikipedia-org-3337	245	5	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	245	6	\sigma	\sigma	CD
en-wikipedia-org-3337	245	7	^	^	NN
en-wikipedia-org-3337	245	8	{	{	-LRB-
en-wikipedia-org-3337	245	9	*	*	NFP
en-wikipedia-org-3337	245	10	}	}	-RRB-
en-wikipedia-org-3337	245	11	}	}	-RRB-
en-wikipedia-org-3337	245	12	is	be	VBZ
en-wikipedia-org-3337	245	13	the	the	DT
en-wikipedia-org-3337	245	14	fixed	fix	VBN
en-wikipedia-org-3337	245	15	point	point	NN
en-wikipedia-org-3337	245	16	we	-PRON-	PRP
en-wikipedia-org-3337	245	17	have	have	VBP
en-wikipedia-org-3337	245	18	:	:	:
en-wikipedia-org-3337	245	19	σ	σ	NNP
en-wikipedia-org-3337	245	20	∗	∗	NNP
en-wikipedia-org-3337	245	21	=	=	SYM
en-wikipedia-org-3337	245	22	f	f	NNP
en-wikipedia-org-3337	245	23	(	(	-LRB-
en-wikipedia-org-3337	245	24	σ	σ	NNP
en-wikipedia-org-3337	245	25	∗	∗	NNP
en-wikipedia-org-3337	245	26	)	)	-RRB-
en-wikipedia-org-3337	245	27	⇒	⇒	CD
en-wikipedia-org-3337	245	28	σ	σ	NNP
en-wikipedia-org-3337	245	29	i	i	NN
en-wikipedia-org-3337	245	30	∗	∗	NNP
en-wikipedia-org-3337	245	31	=	=	SYM
en-wikipedia-org-3337	245	32	f	f	NNP
en-wikipedia-org-3337	245	33	i	i	PRP
en-wikipedia-org-3337	245	34	(	(	-LRB-
en-wikipedia-org-3337	245	35	σ	σ	NNP
en-wikipedia-org-3337	245	36	∗	∗	NNP
en-wikipedia-org-3337	245	37	)	)	-RRB-
en-wikipedia-org-3337	245	38	⇒	⇒	CD
en-wikipedia-org-3337	245	39	σ	σ	NNP
en-wikipedia-org-3337	245	40	i	i	NN
en-wikipedia-org-3337	245	41	∗	∗	NNP
en-wikipedia-org-3337	245	42	=	=	SYM
en-wikipedia-org-3337	245	43	g	g	NNP
en-wikipedia-org-3337	245	44	i	i	NN
en-wikipedia-org-3337	245	45	(	(	-LRB-
en-wikipedia-org-3337	245	46	σ	σ	NNP
en-wikipedia-org-3337	245	47	∗	∗	NNP
en-wikipedia-org-3337	245	48	)	)	-RRB-
en-wikipedia-org-3337	245	49	∑	∑	.
en-wikipedia-org-3337	245	50	a	a	DT
en-wikipedia-org-3337	245	51	∈	∈	NNP
en-wikipedia-org-3337	245	52	A	a	NN
en-wikipedia-org-3337	245	53	i	i	NN
en-wikipedia-org-3337	245	54	g	g	NN
en-wikipedia-org-3337	245	55	i	i	PRP
en-wikipedia-org-3337	245	56	(	(	-LRB-
en-wikipedia-org-3337	245	57	σ	σ	NNP
en-wikipedia-org-3337	245	58	∗	∗	NNP
en-wikipedia-org-3337	245	59	)	)	-RRB-
en-wikipedia-org-3337	245	60	(	(	-LRB-
en-wikipedia-org-3337	245	61	a	a	DT
en-wikipedia-org-3337	245	62	)	)	-RRB-
en-wikipedia-org-3337	245	63	⇒	⇒	CD
en-wikipedia-org-3337	245	64	σ	σ	NNP
en-wikipedia-org-3337	245	65	i	i	NN
en-wikipedia-org-3337	245	66	∗	∗	NNP
en-wikipedia-org-3337	245	67	=	=	NFP
en-wikipedia-org-3337	245	68	1	1	CD
en-wikipedia-org-3337	245	69	C	C	NNP
en-wikipedia-org-3337	245	70	(	(	-LRB-
en-wikipedia-org-3337	245	71	σ	σ	NNP
en-wikipedia-org-3337	245	72	i	i	NN
en-wikipedia-org-3337	245	73	∗	∗	.
en-wikipedia-org-3337	245	74	+	+	SYM
en-wikipedia-org-3337	245	75	Gain	gain	UH
en-wikipedia-org-3337	245	76	i	i	PRP
en-wikipedia-org-3337	245	77	(	(	-LRB-
en-wikipedia-org-3337	245	78	σ	σ	NNP
en-wikipedia-org-3337	245	79	∗	∗	NNP
en-wikipedia-org-3337	245	80	,	,	,
en-wikipedia-org-3337	245	81	⋅	⋅	NNP
en-wikipedia-org-3337	245	82	)	)	-RRB-
en-wikipedia-org-3337	245	83	)	)	-RRB-
en-wikipedia-org-3337	245	84	⇒	⇒	CD
en-wikipedia-org-3337	245	85	C	C	NNP
en-wikipedia-org-3337	245	86	σ	σ	NNP
en-wikipedia-org-3337	245	87	i	i	NN
en-wikipedia-org-3337	245	88	∗	∗	NNP
en-wikipedia-org-3337	245	89	=	=	SYM
en-wikipedia-org-3337	245	90	σ	σ	NNP
en-wikipedia-org-3337	245	91	i	i	NN
en-wikipedia-org-3337	245	92	∗	∗	.
en-wikipedia-org-3337	245	93	+	+	SYM
en-wikipedia-org-3337	245	94	Gain	gain	UH
en-wikipedia-org-3337	245	95	i	i	PRP
en-wikipedia-org-3337	245	96	(	(	-LRB-
en-wikipedia-org-3337	245	97	σ	σ	NNP
en-wikipedia-org-3337	245	98	∗	∗	NNP
en-wikipedia-org-3337	245	99	,	,	,
en-wikipedia-org-3337	245	100	⋅	⋅	NNP
en-wikipedia-org-3337	245	101	)	)	-RRB-
en-wikipedia-org-3337	245	102	⇒	⇒	CD
en-wikipedia-org-3337	245	103	(	(	-LRB-
en-wikipedia-org-3337	245	104	C	C	NNP
en-wikipedia-org-3337	245	105	−	−	NNP
en-wikipedia-org-3337	245	106	1	1	CD
en-wikipedia-org-3337	245	107	)	)	-RRB-
en-wikipedia-org-3337	245	108	σ	σ	NNP
en-wikipedia-org-3337	245	109	i	i	NN
en-wikipedia-org-3337	245	110	∗	∗	.
en-wikipedia-org-3337	245	111	=	=	NFP
en-wikipedia-org-3337	245	112	Gain	gain	UH
en-wikipedia-org-3337	245	113	i	i	PRP
en-wikipedia-org-3337	245	114	(	(	-LRB-
en-wikipedia-org-3337	245	115	σ	σ	NNP
en-wikipedia-org-3337	245	116	∗	∗	NNP
en-wikipedia-org-3337	245	117	,	,	,
en-wikipedia-org-3337	245	118	⋅	⋅	NNP
en-wikipedia-org-3337	245	119	)	)	-RRB-
en-wikipedia-org-3337	245	120	⇒	⇒	CD
en-wikipedia-org-3337	245	121	σ	σ	NNP
en-wikipedia-org-3337	245	122	i	i	NN
en-wikipedia-org-3337	245	123	∗	∗	.
en-wikipedia-org-3337	245	124	=	=	NFP
en-wikipedia-org-3337	245	125	(	(	-LRB-
en-wikipedia-org-3337	245	126	1	1	CD
en-wikipedia-org-3337	245	127	C	c	NN
en-wikipedia-org-3337	245	128	−	−	NNP
en-wikipedia-org-3337	245	129	1	1	CD
en-wikipedia-org-3337	245	130	)	)	-RRB-
en-wikipedia-org-3337	245	131	Gain	gain	VB
en-wikipedia-org-3337	245	132	i	i	PRP
en-wikipedia-org-3337	245	133	(	(	-LRB-
en-wikipedia-org-3337	245	134	σ	σ	NNP
en-wikipedia-org-3337	245	135	∗	∗	NNP
en-wikipedia-org-3337	245	136	,	,	,
en-wikipedia-org-3337	245	137	⋅	⋅	NNP
en-wikipedia-org-3337	245	138	)	)	-RRB-
en-wikipedia-org-3337	245	139	.	.	.
en-wikipedia-org-3337	246	1	{	{	-LRB-
en-wikipedia-org-3337	246	2	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	246	3	{	{	-LRB-
en-wikipedia-org-3337	246	4	\begin{aligned}\sigma	\begin{aligned}\sigma	NNP
en-wikipedia-org-3337	246	5	^{*}=f(\sigma	^{*}=f(\sigma	NNP
en-wikipedia-org-3337	246	6	^{*})&\Rightarrow	^{*})&\Rightarrow	NNP
en-wikipedia-org-3337	246	7	\sigma	\sigma	CD
en-wikipedia-org-3337	246	8	_	_	NNP
en-wikipedia-org-3337	246	9	{	{	-LRB-
en-wikipedia-org-3337	246	10	i}^{*}=f_{i}(\sigma	i}^{*}=f_{i}(\sigma	NNP
en-wikipedia-org-3337	246	11	^{*})\\&\Rightarrow	^{*})\\&\Rightarrow	NNP
en-wikipedia-org-3337	246	12	\sigma	\sigma	CD
en-wikipedia-org-3337	246	13	_	_	NNP
en-wikipedia-org-3337	246	14	{	{	-LRB-
en-wikipedia-org-3337	246	15	i}^{*}={\frac	i}^{*}={\frac	NNP
en-wikipedia-org-3337	246	16	{	{	-LRB-
en-wikipedia-org-3337	246	17	g_{i}(\sigma	g_{i}(\sigma	.
en-wikipedia-org-3337	246	18	^{*})}{\sum	^{*})}{\sum	NNP
en-wikipedia-org-3337	246	19	_	_	NNP
en-wikipedia-org-3337	246	20	{	{	-LRB-
en-wikipedia-org-3337	246	21	a\in	a\in	NNP
en-wikipedia-org-3337	246	22	A_{i}}g_{i}(\sigma	A_{i}}g_{i}(\sigma	NNP
en-wikipedia-org-3337	246	23	^{*})(a)}}\\[6pt]&\Rightarrow	^{*})(a)}}\\[6pt]&\Rightarrow	NFP
en-wikipedia-org-3337	246	24	\sigma	\sigma	CD
en-wikipedia-org-3337	246	25	_	_	NNP
en-wikipedia-org-3337	246	26	{	{	-LRB-
en-wikipedia-org-3337	246	27	i}^{*}={\frac	i}^{*}={\frac	CD
en-wikipedia-org-3337	246	28	{	{	-LRB-
en-wikipedia-org-3337	246	29	1}{C}}\left(\sigma	1}{c}}\left(\sigma	CD
en-wikipedia-org-3337	246	30	_	_	NNP
en-wikipedia-org-3337	246	31	{	{	-LRB-
en-wikipedia-org-3337	246	32	i}^{*}+{\text{Gain}}_{i}(\sigma	i}^{*}+{\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	246	33	^{*},\cdot	^{*},\cdot	NFP
en-wikipedia-org-3337	246	34	)	)	-RRB-
en-wikipedia-org-3337	246	35	\right)\\[6pt]&\Rightarrow	\right)\\[6pt]&\rightarrow	VBP
en-wikipedia-org-3337	246	36	C\sigma	C\sigma	NNP
en-wikipedia-org-3337	246	37	_	_	NNP
en-wikipedia-org-3337	246	38	{	{	-LRB-
en-wikipedia-org-3337	246	39	i}^{*}=\sigma	i}^{*}=\sigma	NNP
en-wikipedia-org-3337	246	40	_	_	NNP
en-wikipedia-org-3337	246	41	{	{	-LRB-
en-wikipedia-org-3337	246	42	i}^{*}+{\text{Gain}}_{i}(\sigma	i}^{*}+{\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	246	43	^{*},\cdot	^{*},\cdot	NFP
en-wikipedia-org-3337	246	44	)	)	-RRB-
en-wikipedia-org-3337	246	45	\\&\Rightarrow	\\&\rightarrow	UH
en-wikipedia-org-3337	246	46	\left(C-1\right)\sigma	\left(C-1\right)\sigma	NNP
en-wikipedia-org-3337	246	47	_	_	NNP
en-wikipedia-org-3337	246	48	{	{	-LRB-
en-wikipedia-org-3337	246	49	i}^{*}={\text{Gain}}_{i}(\sigma	i}^{*}={\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	246	50	^{*},\cdot	^{*},\cdot	NN
en-wikipedia-org-3337	246	51	)	)	-RRB-
en-wikipedia-org-3337	246	52	\\&\Rightarrow	\\&\Rightarrow	VBZ
en-wikipedia-org-3337	246	53	\sigma	\sigma	CD
en-wikipedia-org-3337	246	54	_	_	NNP
en-wikipedia-org-3337	246	55	{	{	-LRB-
en-wikipedia-org-3337	246	56	i}^{*}=\left({\frac	i}^{*}=\left({\frac	NNP
en-wikipedia-org-3337	246	57	{	{	-LRB-
en-wikipedia-org-3337	246	58	1}{C-1}}\right){\text{Gain}}_{i}(\sigma	1}{c-1}}\right){\text{gain}}_{i}(\sigma	CD
en-wikipedia-org-3337	246	59	^{*},\cdot	^{*},\cdot	NFP
en-wikipedia-org-3337	246	60	)	)	-RRB-
en-wikipedia-org-3337	246	61	.\end{aligned	.\end{aligned	NFP
en-wikipedia-org-3337	246	62	}	}	-RRB-
en-wikipedia-org-3337	246	63	}	}	-RRB-
en-wikipedia-org-3337	246	64	}	}	-RRB-
en-wikipedia-org-3337	246	65	Since	since	IN
en-wikipedia-org-3337	246	66	C	c	NN
en-wikipedia-org-3337	246	67	>	>	NN
en-wikipedia-org-3337	246	68	1	1	CD
en-wikipedia-org-3337	246	69	{	{	-LRB-
en-wikipedia-org-3337	246	70	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	246	71	C>1	C>1	NNS
en-wikipedia-org-3337	246	72	}	}	-RRB-
en-wikipedia-org-3337	246	73	we	-PRON-	PRP
en-wikipedia-org-3337	246	74	have	have	VBP
en-wikipedia-org-3337	246	75	that	that	DT
en-wikipedia-org-3337	246	76	σ	σ	NNP
en-wikipedia-org-3337	246	77	i	i	NN
en-wikipedia-org-3337	246	78	∗	∗	.
en-wikipedia-org-3337	246	79	{	{	-LRB-
en-wikipedia-org-3337	246	80	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	246	81	\sigma	\sigma	CD
en-wikipedia-org-3337	246	82	_	_	NNP
en-wikipedia-org-3337	246	83	{	{	-LRB-
en-wikipedia-org-3337	246	84	i}^	i}^	NNP
en-wikipedia-org-3337	246	85	{	{	-LRB-
en-wikipedia-org-3337	246	86	*	*	NFP
en-wikipedia-org-3337	246	87	}	}	-RRB-
en-wikipedia-org-3337	246	88	}	}	-RRB-
en-wikipedia-org-3337	246	89	is	be	VBZ
en-wikipedia-org-3337	246	90	some	some	DT
en-wikipedia-org-3337	246	91	positive	positive	JJ
en-wikipedia-org-3337	246	92	scaling	scaling	NN
en-wikipedia-org-3337	246	93	of	of	IN
en-wikipedia-org-3337	246	94	the	the	DT
en-wikipedia-org-3337	246	95	vector	vector	NN
en-wikipedia-org-3337	246	96	Gain	Gain	NNP
en-wikipedia-org-3337	246	97	i	i	PRP
en-wikipedia-org-3337	246	98	(	(	-LRB-
en-wikipedia-org-3337	246	99	σ	σ	NNP
en-wikipedia-org-3337	246	100	∗	∗	NNP
en-wikipedia-org-3337	246	101	,	,	,
en-wikipedia-org-3337	246	102	⋅	⋅	NNP
en-wikipedia-org-3337	246	103	)	)	-RRB-
en-wikipedia-org-3337	246	104	{	{	-LRB-
en-wikipedia-org-3337	246	105	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	246	106	{	{	-LRB-
en-wikipedia-org-3337	246	107	\text{Gain}}_{i}(\sigma	\text{gain}}_{i}(\sigma	CD
en-wikipedia-org-3337	246	108	^{*},\cdot	^{*},\cdot	NFP
en-wikipedia-org-3337	246	109	)	)	-RRB-
en-wikipedia-org-3337	246	110	}	}	-RRB-
en-wikipedia-org-3337	246	111	.	.	.
en-wikipedia-org-3337	247	1	Now	now	RB
en-wikipedia-org-3337	247	2	we	-PRON-	PRP
en-wikipedia-org-3337	247	3	claim	claim	VBP
en-wikipedia-org-3337	247	4	that	that	IN
en-wikipedia-org-3337	247	5	∀	∀	NNP
en-wikipedia-org-3337	247	6	a	a	DT
en-wikipedia-org-3337	247	7	∈	∈	NNP
en-wikipedia-org-3337	247	8	A	A	NNP
en-wikipedia-org-3337	247	9	i	i	NN
en-wikipedia-org-3337	247	10	:	:	:
en-wikipedia-org-3337	247	11	σ	σ	XX
en-wikipedia-org-3337	247	12	i	i	NN
en-wikipedia-org-3337	247	13	∗	∗	.
en-wikipedia-org-3337	247	14	(	(	-LRB-
en-wikipedia-org-3337	247	15	a	a	LS
en-wikipedia-org-3337	247	16	)	)	-RRB-
en-wikipedia-org-3337	247	17	(	(	-LRB-
en-wikipedia-org-3337	247	18	u	u	NNP
en-wikipedia-org-3337	247	19	i	i	NNP
en-wikipedia-org-3337	247	20	(	(	-LRB-
en-wikipedia-org-3337	247	21	a	a	DT
en-wikipedia-org-3337	247	22	i	i	NN
en-wikipedia-org-3337	247	23	,	,	,
en-wikipedia-org-3337	247	24	σ	σ	NNP
en-wikipedia-org-3337	247	25	−	−	NNP
en-wikipedia-org-3337	247	26	i	i	NN
en-wikipedia-org-3337	247	27	∗	∗	NNP
en-wikipedia-org-3337	247	28	)	)	-RRB-
en-wikipedia-org-3337	247	29	−	−	NNP
en-wikipedia-org-3337	247	30	u	u	NNP
en-wikipedia-org-3337	247	31	i	i	NNP
en-wikipedia-org-3337	247	32	(	(	-LRB-
en-wikipedia-org-3337	247	33	σ	σ	NNP
en-wikipedia-org-3337	247	34	i	i	NN
en-wikipedia-org-3337	247	35	∗	∗	NNP
en-wikipedia-org-3337	247	36	,	,	,
en-wikipedia-org-3337	247	37	σ	σ	NNP
en-wikipedia-org-3337	247	38	−	−	NNP
en-wikipedia-org-3337	247	39	i	i	NN
en-wikipedia-org-3337	247	40	∗	∗	NNP
en-wikipedia-org-3337	247	41	)	)	-RRB-
en-wikipedia-org-3337	247	42	)	)	-RRB-
en-wikipedia-org-3337	247	43	=	=	NFP
en-wikipedia-org-3337	247	44	σ	σ	XX
en-wikipedia-org-3337	247	45	i	i	NN
en-wikipedia-org-3337	247	46	∗	∗	.
en-wikipedia-org-3337	247	47	(	(	-LRB-
en-wikipedia-org-3337	247	48	a	a	LS
en-wikipedia-org-3337	247	49	)	)	-RRB-
en-wikipedia-org-3337	247	50	Gain	gain	NN
en-wikipedia-org-3337	247	51	i	i	PRP
en-wikipedia-org-3337	247	52	(	(	-LRB-
en-wikipedia-org-3337	247	53	σ	σ	NNP
en-wikipedia-org-3337	247	54	∗	∗	NNP
en-wikipedia-org-3337	247	55	,	,	,
en-wikipedia-org-3337	247	56	a	a	LS
en-wikipedia-org-3337	247	57	)	)	-RRB-
en-wikipedia-org-3337	247	58	{	{	-LRB-
en-wikipedia-org-3337	247	59	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	247	60	\forall	\forall	CD
en-wikipedia-org-3337	247	61	a\in	a\in	NNP
en-wikipedia-org-3337	247	62	A_{i}:\quad	A_{i}:\quad	NNPS
en-wikipedia-org-3337	247	63	\sigma	\sigma	CD
en-wikipedia-org-3337	247	64	_	_	NNP
en-wikipedia-org-3337	247	65	{	{	-LRB-
en-wikipedia-org-3337	247	66	i}^{*}(a)(u_{i}(a_{i},\sigma	i}^{*}(a)(u_{i}(a_{i},\sigma	NNP
en-wikipedia-org-3337	247	67	_	_	NNP
en-wikipedia-org-3337	247	68	{	{	-LRB-
en-wikipedia-org-3337	247	69	-i}^{*})-u_{i}(\sigma	-i}^{*})-u_{i}(\sigma	NNP
en-wikipedia-org-3337	247	70	_	_	NNP
en-wikipedia-org-3337	247	71	{	{	-LRB-
en-wikipedia-org-3337	247	72	i}^{*},\sigma	i}^{*},\sigma	NNP
en-wikipedia-org-3337	247	73	_	_	NNP
en-wikipedia-org-3337	247	74	{	{	-LRB-
en-wikipedia-org-3337	247	75	-i}^{*}))=\sigma	-i}^{*}))=\sigma	:
en-wikipedia-org-3337	247	76	_	_	NNP
en-wikipedia-org-3337	247	77	{	{	-LRB-
en-wikipedia-org-3337	247	78	i}^{*}(a){\text{Gain}}_{i}(\sigma	i}^{*}(a){\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	247	79	^{*},a	^{*},a	FW
en-wikipedia-org-3337	247	80	)	)	-RRB-
en-wikipedia-org-3337	247	81	}	}	-RRB-
en-wikipedia-org-3337	247	82	To	to	TO
en-wikipedia-org-3337	247	83	see	see	VB
en-wikipedia-org-3337	247	84	this	this	DT
en-wikipedia-org-3337	247	85	,	,	,
en-wikipedia-org-3337	247	86	we	-PRON-	PRP
en-wikipedia-org-3337	247	87	first	first	RB
en-wikipedia-org-3337	247	88	note	note	VBP
en-wikipedia-org-3337	247	89	that	that	IN
en-wikipedia-org-3337	247	90	if	if	IN
en-wikipedia-org-3337	247	91	Gain	Gain	NNP
en-wikipedia-org-3337	247	92	i	i	PRP
en-wikipedia-org-3337	247	93	(	(	-LRB-
en-wikipedia-org-3337	247	94	σ	σ	NNP
en-wikipedia-org-3337	247	95	∗	∗	NNP
en-wikipedia-org-3337	247	96	,	,	,
en-wikipedia-org-3337	247	97	a	a	LS
en-wikipedia-org-3337	247	98	)	)	-RRB-
en-wikipedia-org-3337	247	99	>	>	XX
en-wikipedia-org-3337	247	100	0	0	NFP
en-wikipedia-org-3337	247	101	{	{	-LRB-
en-wikipedia-org-3337	247	102	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	247	103	{	{	-LRB-
en-wikipedia-org-3337	247	104	\text{Gain}}_{i}(\sigma	\text{gain}}_{i}(\sigma	CD
en-wikipedia-org-3337	247	105	^{*},a)>0	^{*},a)>0	NFP
en-wikipedia-org-3337	247	106	}	}	-RRB-
en-wikipedia-org-3337	247	107	then	then	RB
en-wikipedia-org-3337	247	108	this	this	DT
en-wikipedia-org-3337	247	109	is	be	VBZ
en-wikipedia-org-3337	247	110	true	true	JJ
en-wikipedia-org-3337	247	111	by	by	IN
en-wikipedia-org-3337	247	112	definition	definition	NN
en-wikipedia-org-3337	247	113	of	of	IN
en-wikipedia-org-3337	247	114	the	the	DT
en-wikipedia-org-3337	247	115	gain	gain	NN
en-wikipedia-org-3337	247	116	function	function	NN
en-wikipedia-org-3337	247	117	.	.	.
en-wikipedia-org-3337	248	1	Now	now	RB
en-wikipedia-org-3337	248	2	assume	assume	VB
en-wikipedia-org-3337	248	3	that	that	IN
en-wikipedia-org-3337	248	4	Gain	Gain	NNP
en-wikipedia-org-3337	248	5	i	i	PRP
en-wikipedia-org-3337	248	6	(	(	-LRB-
en-wikipedia-org-3337	248	7	σ	σ	NNP
en-wikipedia-org-3337	248	8	∗	∗	NNP
en-wikipedia-org-3337	248	9	,	,	,
en-wikipedia-org-3337	248	10	a	a	LS
en-wikipedia-org-3337	248	11	)	)	-RRB-
en-wikipedia-org-3337	248	12	=	=	SYM
en-wikipedia-org-3337	248	13	0	0	NFP
en-wikipedia-org-3337	248	14	{	{	-LRB-
en-wikipedia-org-3337	248	15	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	248	16	{	{	-LRB-
en-wikipedia-org-3337	248	17	\text{Gain}}_{i}(\sigma	\text{gain}}_{i}(\sigma	CD
en-wikipedia-org-3337	248	18	^{*},a)=0	^{*},a)=0	,
en-wikipedia-org-3337	248	19	}	}	-RRB-
en-wikipedia-org-3337	248	20	.	.	.
en-wikipedia-org-3337	249	1	By	by	IN
en-wikipedia-org-3337	249	2	our	-PRON-	PRP$
en-wikipedia-org-3337	249	3	previous	previous	JJ
en-wikipedia-org-3337	249	4	statements	statement	NNS
en-wikipedia-org-3337	249	5	we	-PRON-	PRP
en-wikipedia-org-3337	249	6	have	have	VBP
en-wikipedia-org-3337	249	7	that	that	DT
en-wikipedia-org-3337	249	8	σ	σ	NNP
en-wikipedia-org-3337	249	9	i	i	NNP
en-wikipedia-org-3337	249	10	∗	∗	.
en-wikipedia-org-3337	249	11	(	(	-LRB-
en-wikipedia-org-3337	249	12	a	a	LS
en-wikipedia-org-3337	249	13	)	)	-RRB-
en-wikipedia-org-3337	249	14	=	=	NFP
en-wikipedia-org-3337	249	15	(	(	-LRB-
en-wikipedia-org-3337	249	16	1	1	CD
en-wikipedia-org-3337	249	17	C	c	NN
en-wikipedia-org-3337	249	18	−	−	NNP
en-wikipedia-org-3337	249	19	1	1	CD
en-wikipedia-org-3337	249	20	)	)	-RRB-
en-wikipedia-org-3337	249	21	Gain	gain	VB
en-wikipedia-org-3337	249	22	i	i	PRP
en-wikipedia-org-3337	249	23	(	(	-LRB-
en-wikipedia-org-3337	249	24	σ	σ	NNP
en-wikipedia-org-3337	249	25	∗	∗	NNP
en-wikipedia-org-3337	249	26	,	,	,
en-wikipedia-org-3337	249	27	a	a	LS
en-wikipedia-org-3337	249	28	)	)	-RRB-
en-wikipedia-org-3337	249	29	=	=	SYM
en-wikipedia-org-3337	249	30	0	0	NFP
en-wikipedia-org-3337	249	31	{	{	-LRB-
en-wikipedia-org-3337	249	32	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	249	33	\sigma	\sigma	CD
en-wikipedia-org-3337	249	34	_	_	NNP
en-wikipedia-org-3337	249	35	{	{	-LRB-
en-wikipedia-org-3337	249	36	i}^{*}(a)=\left({\frac	i}^{*}(a)=\left({\frac	NNP
en-wikipedia-org-3337	249	37	{	{	-LRB-
en-wikipedia-org-3337	249	38	1}{C-1}}\right){\text{Gain}}_{i}(\sigma	1}{c-1}}\right){\text{gain}}_{i}(\sigma	CD
en-wikipedia-org-3337	249	39	^{*},a)=0	^{*},a)=0	NFP
en-wikipedia-org-3337	249	40	}	}	-RRB-
en-wikipedia-org-3337	249	41	and	and	CC
en-wikipedia-org-3337	249	42	so	so	RB
en-wikipedia-org-3337	249	43	the	the	DT
en-wikipedia-org-3337	249	44	left	left	JJ
en-wikipedia-org-3337	249	45	term	term	NN
en-wikipedia-org-3337	249	46	is	be	VBZ
en-wikipedia-org-3337	249	47	zero	zero	CD
en-wikipedia-org-3337	249	48	,	,	,
en-wikipedia-org-3337	249	49	giving	give	VBG
en-wikipedia-org-3337	249	50	us	-PRON-	PRP
en-wikipedia-org-3337	249	51	that	that	IN
en-wikipedia-org-3337	249	52	the	the	DT
en-wikipedia-org-3337	249	53	entire	entire	JJ
en-wikipedia-org-3337	249	54	expression	expression	NN
en-wikipedia-org-3337	249	55	is	be	VBZ
en-wikipedia-org-3337	249	56	0	0	NFP
en-wikipedia-org-3337	249	57	{	{	-LRB-
en-wikipedia-org-3337	249	58	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	249	59	0	0	CD
en-wikipedia-org-3337	249	60	}	}	-RRB-
en-wikipedia-org-3337	249	61	as	as	IN
en-wikipedia-org-3337	249	62	needed	need	VBN
en-wikipedia-org-3337	249	63	.	.	.
en-wikipedia-org-3337	250	1	So	so	RB
en-wikipedia-org-3337	250	2	we	-PRON-	PRP
en-wikipedia-org-3337	250	3	finally	finally	RB
en-wikipedia-org-3337	250	4	have	have	VBP
en-wikipedia-org-3337	250	5	that	that	DT
en-wikipedia-org-3337	250	6	0	0	CD
en-wikipedia-org-3337	250	7	=	=	SYM
en-wikipedia-org-3337	250	8	u	u	NN
en-wikipedia-org-3337	250	9	i	i	NN
en-wikipedia-org-3337	250	10	(	(	-LRB-
en-wikipedia-org-3337	250	11	σ	σ	NNP
en-wikipedia-org-3337	250	12	i	i	NN
en-wikipedia-org-3337	250	13	∗	∗	NNP
en-wikipedia-org-3337	250	14	,	,	,
en-wikipedia-org-3337	250	15	σ	σ	NNP
en-wikipedia-org-3337	250	16	−	−	NNP
en-wikipedia-org-3337	250	17	i	i	NN
en-wikipedia-org-3337	250	18	∗	∗	NNP
en-wikipedia-org-3337	250	19	)	)	-RRB-
en-wikipedia-org-3337	250	20	−	−	NNP
en-wikipedia-org-3337	250	21	u	u	NNP
en-wikipedia-org-3337	250	22	i	i	NNP
en-wikipedia-org-3337	250	23	(	(	-LRB-
en-wikipedia-org-3337	250	24	σ	σ	NNP
en-wikipedia-org-3337	250	25	i	i	NN
en-wikipedia-org-3337	250	26	∗	∗	NNP
en-wikipedia-org-3337	250	27	,	,	,
en-wikipedia-org-3337	250	28	σ	σ	NNP
en-wikipedia-org-3337	250	29	−	−	NNP
en-wikipedia-org-3337	250	30	i	i	NN
en-wikipedia-org-3337	250	31	∗	∗	NNP
en-wikipedia-org-3337	250	32	)	)	-RRB-
en-wikipedia-org-3337	250	33	=	=	NFP
en-wikipedia-org-3337	250	34	(	(	-LRB-
en-wikipedia-org-3337	250	35	∑	∑	.
en-wikipedia-org-3337	250	36	a	a	DT
en-wikipedia-org-3337	250	37	∈	∈	NNP
en-wikipedia-org-3337	250	38	A	a	NN
en-wikipedia-org-3337	250	39	i	i	NN
en-wikipedia-org-3337	250	40	σ	σ	XX
en-wikipedia-org-3337	250	41	i	i	NN
en-wikipedia-org-3337	250	42	∗	∗	.
en-wikipedia-org-3337	250	43	(	(	-LRB-
en-wikipedia-org-3337	250	44	a	a	LS
en-wikipedia-org-3337	250	45	)	)	-RRB-
en-wikipedia-org-3337	250	46	u	u	NN
en-wikipedia-org-3337	250	47	i	i	NN
en-wikipedia-org-3337	250	48	(	(	-LRB-
en-wikipedia-org-3337	250	49	a	a	DT
en-wikipedia-org-3337	250	50	i	i	NN
en-wikipedia-org-3337	250	51	,	,	,
en-wikipedia-org-3337	250	52	σ	σ	NNP
en-wikipedia-org-3337	250	53	−	−	NNP
en-wikipedia-org-3337	250	54	i	i	NN
en-wikipedia-org-3337	250	55	∗	∗	NNP
en-wikipedia-org-3337	250	56	)	)	-RRB-
en-wikipedia-org-3337	250	57	)	)	-RRB-
en-wikipedia-org-3337	250	58	−	−	NNP
en-wikipedia-org-3337	250	59	u	u	NNP
en-wikipedia-org-3337	250	60	i	i	NNP
en-wikipedia-org-3337	250	61	(	(	-LRB-
en-wikipedia-org-3337	250	62	σ	σ	NNP
en-wikipedia-org-3337	250	63	i	i	NN
en-wikipedia-org-3337	250	64	∗	∗	NNP
en-wikipedia-org-3337	250	65	,	,	,
en-wikipedia-org-3337	250	66	σ	σ	NNP
en-wikipedia-org-3337	250	67	−	−	NNP
en-wikipedia-org-3337	250	68	i	i	NN
en-wikipedia-org-3337	250	69	∗	∗	NNP
en-wikipedia-org-3337	250	70	)	)	-RRB-
en-wikipedia-org-3337	250	71	=	=	NFP
en-wikipedia-org-3337	250	72	∑	∑	.
en-wikipedia-org-3337	250	73	a	a	DT
en-wikipedia-org-3337	250	74	∈	∈	NNP
en-wikipedia-org-3337	250	75	A	a	NN
en-wikipedia-org-3337	250	76	i	i	NN
en-wikipedia-org-3337	250	77	σ	σ	XX
en-wikipedia-org-3337	250	78	i	i	NN
en-wikipedia-org-3337	250	79	∗	∗	.
en-wikipedia-org-3337	250	80	(	(	-LRB-
en-wikipedia-org-3337	250	81	a	a	LS
en-wikipedia-org-3337	250	82	)	)	-RRB-
en-wikipedia-org-3337	250	83	(	(	-LRB-
en-wikipedia-org-3337	250	84	u	u	NNP
en-wikipedia-org-3337	250	85	i	i	NNP
en-wikipedia-org-3337	250	86	(	(	-LRB-
en-wikipedia-org-3337	250	87	a	a	DT
en-wikipedia-org-3337	250	88	i	i	NN
en-wikipedia-org-3337	250	89	,	,	,
en-wikipedia-org-3337	250	90	σ	σ	NNP
en-wikipedia-org-3337	250	91	−	−	NNP
en-wikipedia-org-3337	250	92	i	i	NN
en-wikipedia-org-3337	250	93	∗	∗	NNP
en-wikipedia-org-3337	250	94	)	)	-RRB-
en-wikipedia-org-3337	250	95	−	−	NNP
en-wikipedia-org-3337	250	96	u	u	NNP
en-wikipedia-org-3337	250	97	i	i	NNP
en-wikipedia-org-3337	250	98	(	(	-LRB-
en-wikipedia-org-3337	250	99	σ	σ	NNP
en-wikipedia-org-3337	250	100	i	i	NN
en-wikipedia-org-3337	250	101	∗	∗	NNP
en-wikipedia-org-3337	250	102	,	,	,
en-wikipedia-org-3337	250	103	σ	σ	NNP
en-wikipedia-org-3337	250	104	−	−	NNP
en-wikipedia-org-3337	250	105	i	i	NN
en-wikipedia-org-3337	250	106	∗	∗	NNP
en-wikipedia-org-3337	250	107	)	)	-RRB-
en-wikipedia-org-3337	250	108	)	)	-RRB-
en-wikipedia-org-3337	250	109	=	=	NFP
en-wikipedia-org-3337	250	110	∑	∑	.
en-wikipedia-org-3337	250	111	a	a	DT
en-wikipedia-org-3337	250	112	∈	∈	NNP
en-wikipedia-org-3337	250	113	A	a	NN
en-wikipedia-org-3337	250	114	i	i	NN
en-wikipedia-org-3337	250	115	σ	σ	XX
en-wikipedia-org-3337	250	116	i	i	NN
en-wikipedia-org-3337	250	117	∗	∗	.
en-wikipedia-org-3337	250	118	(	(	-LRB-
en-wikipedia-org-3337	250	119	a	a	LS
en-wikipedia-org-3337	250	120	)	)	-RRB-
en-wikipedia-org-3337	250	121	Gain	gain	NN
en-wikipedia-org-3337	250	122	i	i	PRP
en-wikipedia-org-3337	250	123	(	(	-LRB-
en-wikipedia-org-3337	250	124	σ	σ	NNP
en-wikipedia-org-3337	250	125	∗	∗	NNP
en-wikipedia-org-3337	250	126	,	,	,
en-wikipedia-org-3337	250	127	a	a	LS
en-wikipedia-org-3337	250	128	)	)	-RRB-
en-wikipedia-org-3337	250	129	 	  	_SP
en-wikipedia-org-3337	250	130	by	by	IN
en-wikipedia-org-3337	250	131	the	the	DT
en-wikipedia-org-3337	250	132	previous	previous	JJ
en-wikipedia-org-3337	250	133	statements	statement	NNS
en-wikipedia-org-3337	250	134	  	  	_SP
en-wikipedia-org-3337	250	135	=	=	SYM
en-wikipedia-org-3337	250	136	∑	∑	.
en-wikipedia-org-3337	250	137	a	a	DT
en-wikipedia-org-3337	250	138	∈	∈	NNP
en-wikipedia-org-3337	250	139	A	a	NN
en-wikipedia-org-3337	250	140	i	i	NN
en-wikipedia-org-3337	250	141	(	(	-LRB-
en-wikipedia-org-3337	250	142	C	c	NN
en-wikipedia-org-3337	250	143	−	−	NNP
en-wikipedia-org-3337	250	144	1	1	CD
en-wikipedia-org-3337	250	145	)	)	-RRB-
en-wikipedia-org-3337	250	146	σ	σ	NNP
en-wikipedia-org-3337	250	147	i	i	NN
en-wikipedia-org-3337	250	148	∗	∗	.
en-wikipedia-org-3337	250	149	(	(	-LRB-
en-wikipedia-org-3337	250	150	a	a	DT
en-wikipedia-org-3337	250	151	)	)	-RRB-
en-wikipedia-org-3337	250	152	2	2	CD
en-wikipedia-org-3337	250	153	>	>	NN
en-wikipedia-org-3337	250	154	0	0	CD
en-wikipedia-org-3337	250	155	{	{	-LRB-
en-wikipedia-org-3337	250	156	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	250	157	{	{	-LRB-
en-wikipedia-org-3337	250	158	\begin{aligned}0&=u_{i}(\sigma	\begin{aligned}0&=u_{i}(\sigma	NNP
en-wikipedia-org-3337	250	159	_	_	NNP
en-wikipedia-org-3337	250	160	{	{	-LRB-
en-wikipedia-org-3337	250	161	i}^{*},\sigma	i}^{*},\sigma	NNP
en-wikipedia-org-3337	250	162	_	_	NNP
en-wikipedia-org-3337	250	163	{	{	-LRB-
en-wikipedia-org-3337	250	164	-i}^{*})-u_{i}(\sigma	-i}^{*})-u_{i}(\sigma	NNP
en-wikipedia-org-3337	250	165	_	_	NNP
en-wikipedia-org-3337	250	166	{	{	-LRB-
en-wikipedia-org-3337	250	167	i}^{*},\sigma	i}^{*},\sigma	NNP
en-wikipedia-org-3337	250	168	_	_	NNP
en-wikipedia-org-3337	250	169	{	{	-LRB-
en-wikipedia-org-3337	250	170	-i}^{*})\\&=\left(\sum	-i}^{*})\\&=\left(\sum	NNP
en-wikipedia-org-3337	250	171	_	_	NNP
en-wikipedia-org-3337	250	172	{	{	-LRB-
en-wikipedia-org-3337	250	173	a\in	a\in	NNP
en-wikipedia-org-3337	250	174	A_{i}}\sigma	A_{i}}\sigma	NNP
en-wikipedia-org-3337	250	175	_	_	NNP
en-wikipedia-org-3337	250	176	{	{	-LRB-
en-wikipedia-org-3337	250	177	i}^{*}(a)u_{i}(a_{i},\sigma	i}^{*}(a)u_{i}(a_{i},\sigma	NNP
en-wikipedia-org-3337	250	178	_	_	NNP
en-wikipedia-org-3337	250	179	{	{	-LRB-
en-wikipedia-org-3337	250	180	-i}^{*})\right)-u_{i}(\sigma	-i}^{*})\right)-u_{i}(\sigma	NNP
en-wikipedia-org-3337	250	181	_	_	NNP
en-wikipedia-org-3337	250	182	{	{	-LRB-
en-wikipedia-org-3337	250	183	i}^{*},\sigma	i}^{*},\sigma	NNP
en-wikipedia-org-3337	250	184	_	_	NNP
en-wikipedia-org-3337	250	185	{	{	-LRB-
en-wikipedia-org-3337	250	186	-i}^{*})\\&=\sum	-i}^{*})\\&=\sum	:
en-wikipedia-org-3337	250	187	_	_	NNP
en-wikipedia-org-3337	250	188	{	{	-LRB-
en-wikipedia-org-3337	250	189	a\in	a\in	NNP
en-wikipedia-org-3337	250	190	A_{i}}\sigma	A_{i}}\sigma	NNP
en-wikipedia-org-3337	250	191	_	_	NNP
en-wikipedia-org-3337	250	192	{	{	-LRB-
en-wikipedia-org-3337	250	193	i}^{*}(a)(u_{i}(a_{i},\sigma	i}^{*}(a)(u_{i}(a_{i},\sigma	NNP
en-wikipedia-org-3337	250	194	_	_	NNP
en-wikipedia-org-3337	250	195	{	{	-LRB-
en-wikipedia-org-3337	250	196	-i}^{*})-u_{i}(\sigma	-i}^{*})-u_{i}(\sigma	NNP
en-wikipedia-org-3337	250	197	_	_	NNP
en-wikipedia-org-3337	250	198	{	{	-LRB-
en-wikipedia-org-3337	250	199	i}^{*},\sigma	i}^{*},\sigma	NNP
en-wikipedia-org-3337	250	200	_	_	NNP
en-wikipedia-org-3337	250	201	{	{	-LRB-
en-wikipedia-org-3337	250	202	-i}^{*}))\\&=\sum	-i}^{*}))\\&=\sum	:
en-wikipedia-org-3337	250	203	_	_	NNP
en-wikipedia-org-3337	250	204	{	{	-LRB-
en-wikipedia-org-3337	250	205	a\in	a\in	NNP
en-wikipedia-org-3337	250	206	A_{i}}\sigma	A_{i}}\sigma	NNP
en-wikipedia-org-3337	250	207	_	_	NNP
en-wikipedia-org-3337	250	208	{	{	-LRB-
en-wikipedia-org-3337	250	209	i}^{*}(a){\text{Gain}}_{i}(\sigma	i}^{*}(a){\text{Gain}}_{i}(\sigma	NNP
en-wikipedia-org-3337	250	210	^{*},a)&&{\text	^{*},a)&&{\text	NFP
en-wikipedia-org-3337	250	211	{	{	-LRB-
en-wikipedia-org-3337	250	212	by	by	IN
en-wikipedia-org-3337	250	213	the	the	DT
en-wikipedia-org-3337	250	214	previous	previous	JJ
en-wikipedia-org-3337	250	215	statements	statement	NNS
en-wikipedia-org-3337	250	216	}	}	-RRB-
en-wikipedia-org-3337	250	217	}	}	-RRB-
en-wikipedia-org-3337	250	218	\\&=\sum	\\&=\sum	NN
en-wikipedia-org-3337	250	219	_	_	NNP
en-wikipedia-org-3337	250	220	{	{	-LRB-
en-wikipedia-org-3337	250	221	a\in	a\in	NNP
en-wikipedia-org-3337	250	222	A_{i}}\left(C-1\right)\sigma	A_{i}}\left(C-1\right)\sigma	NNP
en-wikipedia-org-3337	250	223	_	_	NNP
en-wikipedia-org-3337	250	224	{	{	-LRB-
en-wikipedia-org-3337	250	225	i}^{*}(a)^{2}>0\end{aligned	i}^{*}(a)^{2}>0\end{aligned	NNP
en-wikipedia-org-3337	250	226	}	}	-RRB-
en-wikipedia-org-3337	250	227	}	}	-RRB-
en-wikipedia-org-3337	250	228	}	}	-RRB-
en-wikipedia-org-3337	250	229	where	where	WRB
en-wikipedia-org-3337	250	230	the	the	DT
en-wikipedia-org-3337	250	231	last	last	JJ
en-wikipedia-org-3337	250	232	inequality	inequality	NN
en-wikipedia-org-3337	250	233	follows	follow	VBZ
en-wikipedia-org-3337	250	234	since	since	IN
en-wikipedia-org-3337	250	235	σ	σ	NN
en-wikipedia-org-3337	250	236	i	i	NN
en-wikipedia-org-3337	250	237	∗	∗	.
en-wikipedia-org-3337	250	238	{	{	-LRB-
en-wikipedia-org-3337	250	239	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	250	240	\sigma	\sigma	CD
en-wikipedia-org-3337	250	241	_	_	NNP
en-wikipedia-org-3337	250	242	{	{	-LRB-
en-wikipedia-org-3337	250	243	i}^	i}^	NNP
en-wikipedia-org-3337	250	244	{	{	-LRB-
en-wikipedia-org-3337	250	245	*	*	NFP
en-wikipedia-org-3337	250	246	}	}	-RRB-
en-wikipedia-org-3337	250	247	}	}	-RRB-
en-wikipedia-org-3337	250	248	is	be	VBZ
en-wikipedia-org-3337	250	249	a	a	DT
en-wikipedia-org-3337	250	250	non	non	JJ
en-wikipedia-org-3337	250	251	-	-	JJ
en-wikipedia-org-3337	250	252	zero	zero	CD
en-wikipedia-org-3337	250	253	vector	vector	NN
en-wikipedia-org-3337	250	254	.	.	.
en-wikipedia-org-3337	251	1	But	but	CC
en-wikipedia-org-3337	251	2	this	this	DT
en-wikipedia-org-3337	251	3	is	be	VBZ
en-wikipedia-org-3337	251	4	a	a	DT
en-wikipedia-org-3337	251	5	clear	clear	JJ
en-wikipedia-org-3337	251	6	contradiction	contradiction	NN
en-wikipedia-org-3337	251	7	,	,	,
en-wikipedia-org-3337	251	8	so	so	IN
en-wikipedia-org-3337	251	9	all	all	PDT
en-wikipedia-org-3337	251	10	the	the	DT
en-wikipedia-org-3337	251	11	gains	gain	NNS
en-wikipedia-org-3337	251	12	must	must	MD
en-wikipedia-org-3337	251	13	indeed	indeed	RB
en-wikipedia-org-3337	251	14	be	be	VB
en-wikipedia-org-3337	251	15	zero	zero	CD
en-wikipedia-org-3337	251	16	.	.	.
en-wikipedia-org-3337	252	1	Therefore	therefore	RB
en-wikipedia-org-3337	252	2	,	,	,
en-wikipedia-org-3337	252	3	σ	σ	NNP
en-wikipedia-org-3337	252	4	∗	∗	NNP
en-wikipedia-org-3337	252	5	{	{	-LRB-
en-wikipedia-org-3337	252	6	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	252	7	\sigma	\sigma	CD
en-wikipedia-org-3337	252	8	^	^	NN
en-wikipedia-org-3337	252	9	{	{	-LRB-
en-wikipedia-org-3337	252	10	*	*	NFP
en-wikipedia-org-3337	252	11	}	}	-RRB-
en-wikipedia-org-3337	252	12	}	}	-RRB-
en-wikipedia-org-3337	252	13	is	be	VBZ
en-wikipedia-org-3337	252	14	a	a	DT
en-wikipedia-org-3337	252	15	Nash	Nash	NNP
en-wikipedia-org-3337	252	16	equilibrium	equilibrium	NN
en-wikipedia-org-3337	252	17	for	for	IN
en-wikipedia-org-3337	252	18	G	g	NN
en-wikipedia-org-3337	252	19	{	{	-LRB-
en-wikipedia-org-3337	252	20	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	252	21	G	g	NN
en-wikipedia-org-3337	252	22	}	}	-RRB-
en-wikipedia-org-3337	252	23	as	as	IN
en-wikipedia-org-3337	252	24	needed	need	VBN
en-wikipedia-org-3337	252	25	.	.	.
en-wikipedia-org-3337	253	1	Computing	compute	VBG
en-wikipedia-org-3337	253	2	Nash	Nash	NNP
en-wikipedia-org-3337	253	3	equilibria[edit	equilibria[edit	NN
en-wikipedia-org-3337	253	4	]	]	-RRB-
en-wikipedia-org-3337	253	5	If	if	IN
en-wikipedia-org-3337	253	6	a	a	DT
en-wikipedia-org-3337	253	7	player	player	NN
en-wikipedia-org-3337	253	8	A	a	DT
en-wikipedia-org-3337	253	9	has	have	VBZ
en-wikipedia-org-3337	253	10	a	a	DT
en-wikipedia-org-3337	253	11	dominant	dominant	JJ
en-wikipedia-org-3337	253	12	strategy	strategy	NN
en-wikipedia-org-3337	253	13	s	s	NNP
en-wikipedia-org-3337	253	14	A	a	NN
en-wikipedia-org-3337	253	15	{	{	-LRB-
en-wikipedia-org-3337	253	16	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	253	17	s_{A	s_{a	NN
en-wikipedia-org-3337	253	18	}	}	-RRB-
en-wikipedia-org-3337	253	19	}	}	-RRB-
en-wikipedia-org-3337	253	20	then	then	RB
en-wikipedia-org-3337	253	21	there	there	EX
en-wikipedia-org-3337	253	22	exists	exist	VBZ
en-wikipedia-org-3337	253	23	a	a	DT
en-wikipedia-org-3337	253	24	Nash	Nash	NNP
en-wikipedia-org-3337	253	25	equilibrium	equilibrium	NN
en-wikipedia-org-3337	253	26	in	in	IN
en-wikipedia-org-3337	253	27	which	which	WDT
en-wikipedia-org-3337	253	28	A	A	NNP
en-wikipedia-org-3337	253	29	plays	play	VBZ
en-wikipedia-org-3337	253	30	s	s	PRP
en-wikipedia-org-3337	253	31	A	a	NN
en-wikipedia-org-3337	253	32	{	{	-LRB-
en-wikipedia-org-3337	253	33	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	253	34	s_{A	s_{a	NN
en-wikipedia-org-3337	253	35	}	}	-RRB-
en-wikipedia-org-3337	253	36	}	}	-RRB-
en-wikipedia-org-3337	253	37	.	.	.
en-wikipedia-org-3337	254	1	In	in	IN
en-wikipedia-org-3337	254	2	the	the	DT
en-wikipedia-org-3337	254	3	case	case	NN
en-wikipedia-org-3337	254	4	of	of	IN
en-wikipedia-org-3337	254	5	two	two	CD
en-wikipedia-org-3337	254	6	players	player	NNS
en-wikipedia-org-3337	254	7	A	a	NN
en-wikipedia-org-3337	254	8	and	and	CC
en-wikipedia-org-3337	254	9	B	b	NN
en-wikipedia-org-3337	254	10	,	,	,
en-wikipedia-org-3337	254	11	there	there	EX
en-wikipedia-org-3337	254	12	exists	exist	VBZ
en-wikipedia-org-3337	254	13	a	a	DT
en-wikipedia-org-3337	254	14	Nash	Nash	NNP
en-wikipedia-org-3337	254	15	equilibrium	equilibrium	NN
en-wikipedia-org-3337	254	16	in	in	IN
en-wikipedia-org-3337	254	17	which	which	WDT
en-wikipedia-org-3337	254	18	A	A	NNP
en-wikipedia-org-3337	254	19	plays	play	VBZ
en-wikipedia-org-3337	254	20	s	s	PRP
en-wikipedia-org-3337	254	21	A	a	NN
en-wikipedia-org-3337	254	22	{	{	-LRB-
en-wikipedia-org-3337	254	23	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	254	24	s_{A	s_{a	NN
en-wikipedia-org-3337	254	25	}	}	-RRB-
en-wikipedia-org-3337	254	26	}	}	-RRB-
en-wikipedia-org-3337	254	27	and	and	CC
en-wikipedia-org-3337	254	28	B	b	NN
en-wikipedia-org-3337	254	29	plays	play	VBZ
en-wikipedia-org-3337	254	30	a	a	DT
en-wikipedia-org-3337	254	31	best	good	JJS
en-wikipedia-org-3337	254	32	response	response	NN
en-wikipedia-org-3337	254	33	to	to	IN
en-wikipedia-org-3337	254	34	s	s	NN
en-wikipedia-org-3337	254	35	A	a	NN
en-wikipedia-org-3337	254	36	{	{	-LRB-
en-wikipedia-org-3337	254	37	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	254	38	s_{A	s_{a	NN
en-wikipedia-org-3337	254	39	}	}	-RRB-
en-wikipedia-org-3337	254	40	}	}	-RRB-
en-wikipedia-org-3337	254	41	.	.	.
en-wikipedia-org-3337	255	1	If	if	IN
en-wikipedia-org-3337	255	2	s	s	LS
en-wikipedia-org-3337	255	3	A	a	NN
en-wikipedia-org-3337	255	4	{	{	-LRB-
en-wikipedia-org-3337	255	5	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	255	6	s_{A	s_{a	NN
en-wikipedia-org-3337	255	7	}	}	-RRB-
en-wikipedia-org-3337	255	8	}	}	-RRB-
en-wikipedia-org-3337	255	9	is	be	VBZ
en-wikipedia-org-3337	255	10	a	a	DT
en-wikipedia-org-3337	255	11	strictly	strictly	RB
en-wikipedia-org-3337	255	12	dominant	dominant	JJ
en-wikipedia-org-3337	255	13	strategy	strategy	NN
en-wikipedia-org-3337	255	14	,	,	,
en-wikipedia-org-3337	255	15	A	a	DT
en-wikipedia-org-3337	255	16	plays	play	NNS
en-wikipedia-org-3337	255	17	s	s	PRP
en-wikipedia-org-3337	255	18	A	a	NN
en-wikipedia-org-3337	255	19	{	{	-LRB-
en-wikipedia-org-3337	255	20	\displaystyle	\displaystyle	CD
en-wikipedia-org-3337	255	21	s_{A	s_{a	NN
en-wikipedia-org-3337	255	22	}	}	-RRB-
en-wikipedia-org-3337	255	23	}	}	-RRB-
en-wikipedia-org-3337	255	24	in	in	IN
en-wikipedia-org-3337	255	25	all	all	DT
en-wikipedia-org-3337	255	26	Nash	Nash	NNP
en-wikipedia-org-3337	255	27	equilibria	equilibria	NN
en-wikipedia-org-3337	255	28	.	.	.
en-wikipedia-org-3337	256	1	If	if	IN
en-wikipedia-org-3337	256	2	both	both	CC
en-wikipedia-org-3337	256	3	A	A	NNP
en-wikipedia-org-3337	256	4	and	and	CC
en-wikipedia-org-3337	256	5	B	b	NN
en-wikipedia-org-3337	256	6	have	have	VBP
en-wikipedia-org-3337	256	7	strictly	strictly	RB
en-wikipedia-org-3337	256	8	dominant	dominant	JJ
en-wikipedia-org-3337	256	9	strategies	strategy	NNS
en-wikipedia-org-3337	256	10	,	,	,
en-wikipedia-org-3337	256	11	there	there	EX
en-wikipedia-org-3337	256	12	exists	exist	VBZ
en-wikipedia-org-3337	256	13	a	a	DT
en-wikipedia-org-3337	256	14	unique	unique	JJ
en-wikipedia-org-3337	256	15	Nash	Nash	NNP
en-wikipedia-org-3337	256	16	equilibrium	equilibrium	NN
en-wikipedia-org-3337	256	17	in	in	IN
en-wikipedia-org-3337	256	18	which	which	WDT
en-wikipedia-org-3337	256	19	each	each	DT
en-wikipedia-org-3337	256	20	plays	play	VBZ
en-wikipedia-org-3337	256	21	their	-PRON-	PRP$
en-wikipedia-org-3337	256	22	strictly	strictly	RB
en-wikipedia-org-3337	256	23	dominant	dominant	JJ
en-wikipedia-org-3337	256	24	strategy	strategy	NN
en-wikipedia-org-3337	256	25	.	.	.
en-wikipedia-org-3337	257	1	In	in	IN
en-wikipedia-org-3337	257	2	games	game	NNS
en-wikipedia-org-3337	257	3	with	with	IN
en-wikipedia-org-3337	257	4	mixed	mix	VBN
en-wikipedia-org-3337	257	5	-	-	HYPH
en-wikipedia-org-3337	257	6	strategy	strategy	NN
en-wikipedia-org-3337	257	7	Nash	Nash	NNP
en-wikipedia-org-3337	257	8	equilibria	equilibria	NN
en-wikipedia-org-3337	257	9	,	,	,
en-wikipedia-org-3337	257	10	the	the	DT
en-wikipedia-org-3337	257	11	probability	probability	NN
en-wikipedia-org-3337	257	12	of	of	IN
en-wikipedia-org-3337	257	13	a	a	DT
en-wikipedia-org-3337	257	14	player	player	NN
en-wikipedia-org-3337	257	15	choosing	choose	VBG
en-wikipedia-org-3337	257	16	any	any	DT
en-wikipedia-org-3337	257	17	particular	particular	JJ
en-wikipedia-org-3337	257	18	(	(	-LRB-
en-wikipedia-org-3337	257	19	so	so	RB
en-wikipedia-org-3337	257	20	pure	pure	JJ
en-wikipedia-org-3337	257	21	)	)	-RRB-
en-wikipedia-org-3337	257	22	strategy	strategy	NN
en-wikipedia-org-3337	257	23	can	can	MD
en-wikipedia-org-3337	257	24	be	be	VB
en-wikipedia-org-3337	257	25	computed	compute	VBN
en-wikipedia-org-3337	257	26	by	by	IN
en-wikipedia-org-3337	257	27	assigning	assign	VBG
en-wikipedia-org-3337	257	28	a	a	DT
en-wikipedia-org-3337	257	29	variable	variable	NN
en-wikipedia-org-3337	257	30	to	to	IN
en-wikipedia-org-3337	257	31	each	each	DT
en-wikipedia-org-3337	257	32	strategy	strategy	NN
en-wikipedia-org-3337	257	33	that	that	WDT
en-wikipedia-org-3337	257	34	represents	represent	VBZ
en-wikipedia-org-3337	257	35	a	a	DT
en-wikipedia-org-3337	257	36	fixed	fix	VBN
en-wikipedia-org-3337	257	37	probability	probability	NN
en-wikipedia-org-3337	257	38	for	for	IN
en-wikipedia-org-3337	257	39	choosing	choose	VBG
en-wikipedia-org-3337	257	40	that	that	DT
en-wikipedia-org-3337	257	41	strategy	strategy	NN
en-wikipedia-org-3337	257	42	.	.	.
en-wikipedia-org-3337	258	1	In	in	IN
en-wikipedia-org-3337	258	2	order	order	NN
en-wikipedia-org-3337	258	3	for	for	IN
en-wikipedia-org-3337	258	4	a	a	DT
en-wikipedia-org-3337	258	5	player	player	NN
en-wikipedia-org-3337	258	6	to	to	TO
en-wikipedia-org-3337	258	7	be	be	VB
en-wikipedia-org-3337	258	8	willing	willing	JJ
en-wikipedia-org-3337	258	9	to	to	TO
en-wikipedia-org-3337	258	10	randomize	randomize	VB
en-wikipedia-org-3337	258	11	,	,	,
en-wikipedia-org-3337	258	12	their	-PRON-	PRP$
en-wikipedia-org-3337	258	13	expected	expect	VBN
en-wikipedia-org-3337	258	14	payoff	payoff	NN
en-wikipedia-org-3337	258	15	for	for	IN
en-wikipedia-org-3337	258	16	each	each	DT
en-wikipedia-org-3337	258	17	(	(	-LRB-
en-wikipedia-org-3337	258	18	pure	pure	JJ
en-wikipedia-org-3337	258	19	)	)	-RRB-
en-wikipedia-org-3337	258	20	strategy	strategy	NN
en-wikipedia-org-3337	258	21	should	should	MD
en-wikipedia-org-3337	258	22	be	be	VB
en-wikipedia-org-3337	258	23	the	the	DT
en-wikipedia-org-3337	258	24	same	same	JJ
en-wikipedia-org-3337	258	25	.	.	.
en-wikipedia-org-3337	259	1	In	in	IN
en-wikipedia-org-3337	259	2	addition	addition	NN
en-wikipedia-org-3337	259	3	,	,	,
en-wikipedia-org-3337	259	4	the	the	DT
en-wikipedia-org-3337	259	5	sum	sum	NN
en-wikipedia-org-3337	259	6	of	of	IN
en-wikipedia-org-3337	259	7	the	the	DT
en-wikipedia-org-3337	259	8	probabilities	probability	NNS
en-wikipedia-org-3337	259	9	for	for	IN
en-wikipedia-org-3337	259	10	each	each	DT
en-wikipedia-org-3337	259	11	strategy	strategy	NN
en-wikipedia-org-3337	259	12	of	of	IN
en-wikipedia-org-3337	259	13	a	a	DT
en-wikipedia-org-3337	259	14	particular	particular	JJ
en-wikipedia-org-3337	259	15	player	player	NN
en-wikipedia-org-3337	259	16	should	should	MD
en-wikipedia-org-3337	259	17	be	be	VB
en-wikipedia-org-3337	259	18	1	1	CD
en-wikipedia-org-3337	259	19	.	.	.
en-wikipedia-org-3337	260	1	This	this	DT
en-wikipedia-org-3337	260	2	creates	create	VBZ
en-wikipedia-org-3337	260	3	a	a	DT
en-wikipedia-org-3337	260	4	system	system	NN
en-wikipedia-org-3337	260	5	of	of	IN
en-wikipedia-org-3337	260	6	equations	equation	NNS
en-wikipedia-org-3337	260	7	from	from	IN
en-wikipedia-org-3337	260	8	which	which	WDT
en-wikipedia-org-3337	260	9	the	the	DT
en-wikipedia-org-3337	260	10	probabilities	probability	NNS
en-wikipedia-org-3337	260	11	of	of	IN
en-wikipedia-org-3337	260	12	choosing	choose	VBG
en-wikipedia-org-3337	260	13	each	each	DT
en-wikipedia-org-3337	260	14	strategy	strategy	NN
en-wikipedia-org-3337	260	15	can	can	MD
en-wikipedia-org-3337	260	16	be	be	VB
en-wikipedia-org-3337	260	17	derived	derive	VBN
en-wikipedia-org-3337	260	18	.	.	.
en-wikipedia-org-3337	261	1	[	[	-LRB-
en-wikipedia-org-3337	261	2	14	14	CD
en-wikipedia-org-3337	261	3	]	]	-RRB-
en-wikipedia-org-3337	261	4	Examples[edit	examples[edit	LS
en-wikipedia-org-3337	261	5	]	]	-RRB-
en-wikipedia-org-3337	261	6	Matching	Matching	NNP
en-wikipedia-org-3337	261	7	pennies	penny	NNS
en-wikipedia-org-3337	261	8	Player	Player	NNP
en-wikipedia-org-3337	261	9	B	B	NNP
en-wikipedia-org-3337	261	10	Player	Player	NNP
en-wikipedia-org-3337	261	11	A	A	NNP
en-wikipedia-org-3337	261	12	Player	Player	NNP
en-wikipedia-org-3337	261	13	B	B	NNP
en-wikipedia-org-3337	261	14	plays	play	VBZ
en-wikipedia-org-3337	261	15	H	H	NNP
en-wikipedia-org-3337	261	16	Player	Player	NNP
en-wikipedia-org-3337	261	17	B	B	NNP
en-wikipedia-org-3337	261	18	plays	play	VBZ
en-wikipedia-org-3337	261	19	T	T	NNP
en-wikipedia-org-3337	261	20	Player	Player	NNP
en-wikipedia-org-3337	261	21	A	A	NNP
en-wikipedia-org-3337	261	22	plays	play	VBZ
en-wikipedia-org-3337	261	23	H	H	NNP
en-wikipedia-org-3337	261	24	−1	−1	NNP
en-wikipedia-org-3337	261	25	,	,	,
en-wikipedia-org-3337	261	26	+1	+1	NFP
en-wikipedia-org-3337	261	27	+1	+1	NNS
en-wikipedia-org-3337	261	28	,	,	,
en-wikipedia-org-3337	261	29	−1	−1	NNP
en-wikipedia-org-3337	261	30	Player	Player	NNP
en-wikipedia-org-3337	261	31	A	A	NNP
en-wikipedia-org-3337	261	32	plays	play	VBZ
en-wikipedia-org-3337	261	33	T	t	NN
en-wikipedia-org-3337	261	34	+1	+1	NNS
en-wikipedia-org-3337	261	35	,	,	,
en-wikipedia-org-3337	261	36	−1	−1	NNP
en-wikipedia-org-3337	261	37	−1	−1	NNP
en-wikipedia-org-3337	261	38	,	,	,
en-wikipedia-org-3337	261	39	+1	+1	NNS
en-wikipedia-org-3337	261	40	In	in	IN
en-wikipedia-org-3337	261	41	the	the	DT
en-wikipedia-org-3337	261	42	matching	match	VBG
en-wikipedia-org-3337	261	43	pennies	penny	NNS
en-wikipedia-org-3337	261	44	game	game	NN
en-wikipedia-org-3337	261	45	,	,	,
en-wikipedia-org-3337	261	46	player	player	NN
en-wikipedia-org-3337	261	47	A	a	DT
en-wikipedia-org-3337	261	48	loses	lose	VBZ
en-wikipedia-org-3337	261	49	a	a	DT
en-wikipedia-org-3337	261	50	point	point	NN
en-wikipedia-org-3337	261	51	to	to	IN
en-wikipedia-org-3337	261	52	B	b	NN
en-wikipedia-org-3337	261	53	if	if	IN
en-wikipedia-org-3337	261	54	A	a	NN
en-wikipedia-org-3337	261	55	and	and	CC
en-wikipedia-org-3337	261	56	B	b	NN
en-wikipedia-org-3337	261	57	play	play	VB
en-wikipedia-org-3337	261	58	the	the	DT
en-wikipedia-org-3337	261	59	same	same	JJ
en-wikipedia-org-3337	261	60	strategy	strategy	NN
en-wikipedia-org-3337	261	61	and	and	CC
en-wikipedia-org-3337	261	62	wins	win	VBZ
en-wikipedia-org-3337	261	63	a	a	DT
en-wikipedia-org-3337	261	64	point	point	NN
en-wikipedia-org-3337	261	65	from	from	IN
en-wikipedia-org-3337	261	66	B	b	NN
en-wikipedia-org-3337	261	67	if	if	IN
en-wikipedia-org-3337	261	68	they	-PRON-	PRP
en-wikipedia-org-3337	261	69	play	play	VBP
en-wikipedia-org-3337	261	70	different	different	JJ
en-wikipedia-org-3337	261	71	strategies	strategy	NNS
en-wikipedia-org-3337	261	72	.	.	.
en-wikipedia-org-3337	262	1	To	to	TO
en-wikipedia-org-3337	262	2	compute	compute	VB
en-wikipedia-org-3337	262	3	the	the	DT
en-wikipedia-org-3337	262	4	mixed	mix	VBN
en-wikipedia-org-3337	262	5	-	-	HYPH
en-wikipedia-org-3337	262	6	strategy	strategy	NN
en-wikipedia-org-3337	262	7	Nash	Nash	NNP
en-wikipedia-org-3337	262	8	equilibrium	equilibrium	NN
en-wikipedia-org-3337	262	9	,	,	,
en-wikipedia-org-3337	262	10	assign	assign	VB
en-wikipedia-org-3337	262	11	A	a	DT
en-wikipedia-org-3337	262	12	the	the	DT
en-wikipedia-org-3337	262	13	probability	probability	NN
en-wikipedia-org-3337	262	14	p	p	NN
en-wikipedia-org-3337	262	15	of	of	IN
en-wikipedia-org-3337	262	16	playing	play	VBG
en-wikipedia-org-3337	262	17	H	h	NN
en-wikipedia-org-3337	262	18	and	and	CC
en-wikipedia-org-3337	262	19	(	(	-LRB-
en-wikipedia-org-3337	262	20	1−p	1−p	LS
en-wikipedia-org-3337	262	21	)	)	-RRB-
en-wikipedia-org-3337	262	22	of	of	IN
en-wikipedia-org-3337	262	23	playing	play	VBG
en-wikipedia-org-3337	262	24	T	T	NNP
en-wikipedia-org-3337	262	25	,	,	,
en-wikipedia-org-3337	262	26	and	and	CC
en-wikipedia-org-3337	262	27	assign	assign	NN
en-wikipedia-org-3337	262	28	B	B	NNP
en-wikipedia-org-3337	262	29	the	the	DT
en-wikipedia-org-3337	262	30	probability	probability	NN
en-wikipedia-org-3337	262	31	q	q	NN
en-wikipedia-org-3337	262	32	of	of	IN
en-wikipedia-org-3337	262	33	playing	play	VBG
en-wikipedia-org-3337	262	34	H	h	NN
en-wikipedia-org-3337	262	35	and	and	CC
en-wikipedia-org-3337	262	36	(	(	-LRB-
en-wikipedia-org-3337	262	37	1−q	1−q	CD
en-wikipedia-org-3337	262	38	)	)	-RRB-
en-wikipedia-org-3337	262	39	of	of	IN
en-wikipedia-org-3337	262	40	playing	play	VBG
en-wikipedia-org-3337	262	41	T.	T.	NNP
en-wikipedia-org-3337	262	42	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	43	for	for	IN
en-wikipedia-org-3337	262	44	A	a	DT
en-wikipedia-org-3337	262	45	playing	play	VBG
en-wikipedia-org-3337	262	46	H	h	NN
en-wikipedia-org-3337	262	47	]	]	-RRB-
en-wikipedia-org-3337	262	48	=	=	NFP
en-wikipedia-org-3337	262	49	(	(	-LRB-
en-wikipedia-org-3337	262	50	−1)q	−1)q	NFP
en-wikipedia-org-3337	262	51	+	+	CC
en-wikipedia-org-3337	262	52	(	(	-LRB-
en-wikipedia-org-3337	262	53	+1)(1−q	+1)(1−q	NN
en-wikipedia-org-3337	262	54	)	)	-RRB-
en-wikipedia-org-3337	262	55	=	=	NFP
en-wikipedia-org-3337	262	56	1−2q	1−2q	CD
en-wikipedia-org-3337	262	57	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	58	for	for	IN
en-wikipedia-org-3337	262	59	A	a	DT
en-wikipedia-org-3337	262	60	playing	play	VBG
en-wikipedia-org-3337	262	61	T	t	NN
en-wikipedia-org-3337	262	62	]	]	-RRB-
en-wikipedia-org-3337	262	63	=	=	NN
en-wikipedia-org-3337	262	64	(	(	-LRB-
en-wikipedia-org-3337	262	65	+1)q	+1)q	XX
en-wikipedia-org-3337	262	66	+	+	SYM
en-wikipedia-org-3337	262	67	(	(	-LRB-
en-wikipedia-org-3337	262	68	−1)(1−q	−1)(1−q	NN
en-wikipedia-org-3337	262	69	)	)	-RRB-
en-wikipedia-org-3337	262	70	=	=	NFP
en-wikipedia-org-3337	262	71	2q−1	2q−1	CD
en-wikipedia-org-3337	262	72	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	73	for	for	IN
en-wikipedia-org-3337	262	74	A	a	DT
en-wikipedia-org-3337	262	75	playing	play	VBG
en-wikipedia-org-3337	262	76	H	h	NN
en-wikipedia-org-3337	262	77	]	]	-RRB-
en-wikipedia-org-3337	262	78	=	=	-RRB-
en-wikipedia-org-3337	262	79	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	80	for	for	IN
en-wikipedia-org-3337	262	81	A	a	DT
en-wikipedia-org-3337	262	82	playing	play	VBG
en-wikipedia-org-3337	262	83	T	t	NN
en-wikipedia-org-3337	262	84	]	]	-RRB-
en-wikipedia-org-3337	262	85	⇒	⇒	CD
en-wikipedia-org-3337	262	86	1−2q	1−2q	CD
en-wikipedia-org-3337	262	87	=	=	SYM
en-wikipedia-org-3337	262	88	2q−1	2q−1	CD
en-wikipedia-org-3337	262	89	⇒	⇒	CD
en-wikipedia-org-3337	262	90	q	q	NN
en-wikipedia-org-3337	262	91	=	=	SYM
en-wikipedia-org-3337	262	92	1/2	1/2	CD
en-wikipedia-org-3337	262	93	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	94	for	for	IN
en-wikipedia-org-3337	262	95	B	b	NN
en-wikipedia-org-3337	262	96	playing	play	VBG
en-wikipedia-org-3337	262	97	H	h	NN
en-wikipedia-org-3337	262	98	]	]	-RRB-
en-wikipedia-org-3337	262	99	=	=	NN
en-wikipedia-org-3337	262	100	(	(	-LRB-
en-wikipedia-org-3337	262	101	+1)p	+1)p	NFP
en-wikipedia-org-3337	262	102	+	+	SYM
en-wikipedia-org-3337	262	103	(	(	-LRB-
en-wikipedia-org-3337	262	104	−1)(1−p	−1)(1−p	NNP
en-wikipedia-org-3337	262	105	)	)	-RRB-
en-wikipedia-org-3337	262	106	=	=	NFP
en-wikipedia-org-3337	262	107	2p−1	2p−1	CD
en-wikipedia-org-3337	262	108	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	109	for	for	IN
en-wikipedia-org-3337	262	110	B	b	NN
en-wikipedia-org-3337	262	111	playing	play	VBG
en-wikipedia-org-3337	262	112	T	T	NNP
en-wikipedia-org-3337	262	113	]	]	-RRB-
en-wikipedia-org-3337	262	114	=	=	NN
en-wikipedia-org-3337	262	115	(	(	-LRB-
en-wikipedia-org-3337	262	116	−1)p	−1)p	XX
en-wikipedia-org-3337	262	117	+	+	SYM
en-wikipedia-org-3337	262	118	(	(	-LRB-
en-wikipedia-org-3337	262	119	+1)(1−p	+1)(1−p	NN
en-wikipedia-org-3337	262	120	)	)	-RRB-
en-wikipedia-org-3337	262	121	=	=	NFP
en-wikipedia-org-3337	262	122	1−2p	1−2p	CD
en-wikipedia-org-3337	262	123	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	124	for	for	IN
en-wikipedia-org-3337	262	125	B	b	NN
en-wikipedia-org-3337	262	126	playing	play	VBG
en-wikipedia-org-3337	262	127	H	h	NN
en-wikipedia-org-3337	262	128	]	]	-RRB-
en-wikipedia-org-3337	262	129	=	=	-RRB-
en-wikipedia-org-3337	262	130	E[payoff	e[payoff	NN
en-wikipedia-org-3337	262	131	for	for	IN
en-wikipedia-org-3337	262	132	B	b	NN
en-wikipedia-org-3337	262	133	playing	play	VBG
en-wikipedia-org-3337	262	134	T	T	NNP
en-wikipedia-org-3337	262	135	]	]	-RRB-
en-wikipedia-org-3337	262	136	⇒	⇒	CD
en-wikipedia-org-3337	262	137	2p−1	2p−1	CD
en-wikipedia-org-3337	262	138	=	=	SYM
en-wikipedia-org-3337	262	139	1−2p	1−2p	CD
en-wikipedia-org-3337	262	140	⇒	⇒	CD
en-wikipedia-org-3337	262	141	p	p	NN
en-wikipedia-org-3337	262	142	=	=	SYM
en-wikipedia-org-3337	262	143	1/2	1/2	CD
en-wikipedia-org-3337	262	144	Thus	thus	RB
en-wikipedia-org-3337	262	145	a	a	DT
en-wikipedia-org-3337	262	146	mixed	mix	VBN
en-wikipedia-org-3337	262	147	-	-	HYPH
en-wikipedia-org-3337	262	148	strategy	strategy	NN
en-wikipedia-org-3337	262	149	Nash	Nash	NNP
en-wikipedia-org-3337	262	150	equilibrium	equilibrium	NN
en-wikipedia-org-3337	262	151	,	,	,
en-wikipedia-org-3337	262	152	in	in	IN
en-wikipedia-org-3337	262	153	this	this	DT
en-wikipedia-org-3337	262	154	game	game	NN
en-wikipedia-org-3337	262	155	,	,	,
en-wikipedia-org-3337	262	156	is	be	VBZ
en-wikipedia-org-3337	262	157	for	for	IN
en-wikipedia-org-3337	262	158	each	each	DT
en-wikipedia-org-3337	262	159	player	player	NN
en-wikipedia-org-3337	262	160	to	to	TO
en-wikipedia-org-3337	262	161	randomly	randomly	RB
en-wikipedia-org-3337	262	162	choose	choose	VB
en-wikipedia-org-3337	262	163	H	h	NN
en-wikipedia-org-3337	262	164	or	or	CC
en-wikipedia-org-3337	262	165	T	t	NN
en-wikipedia-org-3337	262	166	with	with	IN
en-wikipedia-org-3337	262	167	p	p	NN
en-wikipedia-org-3337	262	168	=	=	SYM
en-wikipedia-org-3337	262	169	1/2	1/2	CD
en-wikipedia-org-3337	262	170	and	and	CC
en-wikipedia-org-3337	262	171	q	q	NN
en-wikipedia-org-3337	262	172	=	=	SYM
en-wikipedia-org-3337	262	173	1/2	1/2	CD
en-wikipedia-org-3337	262	174	.	.	.
en-wikipedia-org-3337	263	1	See	see	VB
en-wikipedia-org-3337	263	2	also[edit	also[edit	LS
en-wikipedia-org-3337	263	3	]	]	-RRB-
en-wikipedia-org-3337	263	4	Adjusted	adjust	VBN
en-wikipedia-org-3337	263	5	winner	winner	NN
en-wikipedia-org-3337	263	6	procedure	procedure	NN
en-wikipedia-org-3337	263	7	Complementarity	complementarity	NN
en-wikipedia-org-3337	263	8	theory	theory	NN
en-wikipedia-org-3337	263	9	Conflict	conflict	NN
en-wikipedia-org-3337	263	10	resolution	resolution	NN
en-wikipedia-org-3337	263	11	research	research	NN
en-wikipedia-org-3337	263	12	Cooperation	Cooperation	NNP
en-wikipedia-org-3337	263	13	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	263	14	selection	selection	NN
en-wikipedia-org-3337	263	15	Evolutionarily	evolutionarily	RB
en-wikipedia-org-3337	263	16	stable	stable	JJ
en-wikipedia-org-3337	263	17	strategy	strategy	NN
en-wikipedia-org-3337	263	18	 	  	_SP
en-wikipedia-org-3337	263	19	–	–	:
en-wikipedia-org-3337	263	20	Strategy	strategy	NN
en-wikipedia-org-3337	263	21	which	which	WDT
en-wikipedia-org-3337	263	22	,	,	,
en-wikipedia-org-3337	263	23	if	if	IN
en-wikipedia-org-3337	263	24	adopted	adopt	VBN
en-wikipedia-org-3337	263	25	by	by	IN
en-wikipedia-org-3337	263	26	a	a	DT
en-wikipedia-org-3337	263	27	population	population	NN
en-wikipedia-org-3337	263	28	in	in	IN
en-wikipedia-org-3337	263	29	a	a	DT
en-wikipedia-org-3337	263	30	given	give	VBN
en-wikipedia-org-3337	263	31	environment	environment	NN
en-wikipedia-org-3337	263	32	,	,	,
en-wikipedia-org-3337	263	33	can	can	MD
en-wikipedia-org-3337	263	34	not	not	RB
en-wikipedia-org-3337	263	35	be	be	VB
en-wikipedia-org-3337	263	36	invaded	invade	VBN
en-wikipedia-org-3337	263	37	by	by	IN
en-wikipedia-org-3337	263	38	any	any	DT
en-wikipedia-org-3337	263	39	alternative	alternative	JJ
en-wikipedia-org-3337	263	40	strategy	strategy	NN
en-wikipedia-org-3337	263	41	that	that	WDT
en-wikipedia-org-3337	263	42	is	be	VBZ
en-wikipedia-org-3337	263	43	initially	initially	RB
en-wikipedia-org-3337	263	44	rare	rare	JJ
en-wikipedia-org-3337	263	45	Glossary	Glossary	NNP
en-wikipedia-org-3337	263	46	of	of	IN
en-wikipedia-org-3337	263	47	game	game	NN
en-wikipedia-org-3337	263	48	theory	theory	NN
en-wikipedia-org-3337	263	49	 	  	_SP
en-wikipedia-org-3337	263	50	–	–	:
en-wikipedia-org-3337	263	51	List	list	NN
en-wikipedia-org-3337	263	52	of	of	IN
en-wikipedia-org-3337	263	53	definitions	definition	NNS
en-wikipedia-org-3337	263	54	of	of	IN
en-wikipedia-org-3337	263	55	terms	term	NNS
en-wikipedia-org-3337	263	56	and	and	CC
en-wikipedia-org-3337	263	57	concepts	concept	NNS
en-wikipedia-org-3337	263	58	used	use	VBN
en-wikipedia-org-3337	263	59	in	in	IN
en-wikipedia-org-3337	263	60	game	game	NN
en-wikipedia-org-3337	263	61	theory	theory	NN
en-wikipedia-org-3337	263	62	Hotelling	hotelle	VBG
en-wikipedia-org-3337	263	63	's	's	POS
en-wikipedia-org-3337	263	64	law	law	NN
en-wikipedia-org-3337	263	65	Manipulated	manipulate	VBD
en-wikipedia-org-3337	263	66	Nash	Nash	NNP
en-wikipedia-org-3337	263	67	equilibrium	equilibrium	NN
en-wikipedia-org-3337	263	68	Mexican	mexican	JJ
en-wikipedia-org-3337	263	69	standoff	standoff	NN
en-wikipedia-org-3337	263	70	Minimax	Minimax	NNP
en-wikipedia-org-3337	263	71	theorem	theorem	NN
en-wikipedia-org-3337	263	72	 	  	_SP
en-wikipedia-org-3337	263	73	–	–	:
en-wikipedia-org-3337	263	74	Gives	give	VBZ
en-wikipedia-org-3337	263	75	conditions	condition	NNS
en-wikipedia-org-3337	263	76	that	that	WDT
en-wikipedia-org-3337	263	77	guarantee	guarantee	VBP
en-wikipedia-org-3337	263	78	the	the	DT
en-wikipedia-org-3337	263	79	max	max	NNP
en-wikipedia-org-3337	263	80	–	–	:
en-wikipedia-org-3337	263	81	min	min	NNP
en-wikipedia-org-3337	263	82	inequality	inequality	NN
en-wikipedia-org-3337	263	83	is	be	VBZ
en-wikipedia-org-3337	263	84	also	also	RB
en-wikipedia-org-3337	263	85	an	an	DT
en-wikipedia-org-3337	263	86	equality	equality	NN
en-wikipedia-org-3337	263	87	Mutual	mutual	JJ
en-wikipedia-org-3337	263	88	assured	assure	VBN
en-wikipedia-org-3337	263	89	destruction	destruction	NN
en-wikipedia-org-3337	263	90	 	  	_SP
en-wikipedia-org-3337	263	91	–	–	:
en-wikipedia-org-3337	263	92	Doctrine	Doctrine	NNP
en-wikipedia-org-3337	263	93	of	of	IN
en-wikipedia-org-3337	263	94	military	military	JJ
en-wikipedia-org-3337	263	95	strategy	strategy	NN
en-wikipedia-org-3337	263	96	Extended	Extended	NNP
en-wikipedia-org-3337	263	97	Mathematical	Mathematical	NNP
en-wikipedia-org-3337	263	98	Programming	Programming	NNP
en-wikipedia-org-3337	263	99	for	for	IN
en-wikipedia-org-3337	263	100	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	263	101	Problems	Problems	NNPS
en-wikipedia-org-3337	263	102	Optimum	optimum	JJ
en-wikipedia-org-3337	263	103	contract	contract	NN
en-wikipedia-org-3337	263	104	and	and	CC
en-wikipedia-org-3337	263	105	par	par	NN
en-wikipedia-org-3337	263	106	contract	contract	NN
en-wikipedia-org-3337	263	107	Self	self	NN
en-wikipedia-org-3337	263	108	-	-	HYPH
en-wikipedia-org-3337	263	109	confirming	confirm	VBG
en-wikipedia-org-3337	263	110	equilibrium	equilibrium	NN
en-wikipedia-org-3337	263	111	Solution	Solution	NNP
en-wikipedia-org-3337	263	112	concept	concept	NN
en-wikipedia-org-3337	263	113	Stackelberg	Stackelberg	NNP
en-wikipedia-org-3337	263	114	competition	competition	NN
en-wikipedia-org-3337	263	115	 	  	_SP
en-wikipedia-org-3337	263	116	–	–	:
en-wikipedia-org-3337	263	117	Economic	economic	JJ
en-wikipedia-org-3337	263	118	model	model	NN
en-wikipedia-org-3337	263	119	Wardrop	Wardrop	NNP
en-wikipedia-org-3337	263	120	's	's	POS
en-wikipedia-org-3337	263	121	principle	principle	NN
en-wikipedia-org-3337	263	122	Notes[edit	notes[edit	NN
en-wikipedia-org-3337	263	123	]	]	-RRB-
en-wikipedia-org-3337	263	124	^	^	NN
en-wikipedia-org-3337	263	125	Osborne	Osborne	NNP
en-wikipedia-org-3337	263	126	,	,	,
en-wikipedia-org-3337	263	127	Martin	Martin	NNP
en-wikipedia-org-3337	263	128	J.	J.	NNP
en-wikipedia-org-3337	263	129	;	;	:
en-wikipedia-org-3337	263	130	Rubinstein	Rubinstein	NNP
en-wikipedia-org-3337	263	131	,	,	,
en-wikipedia-org-3337	263	132	Ariel	Ariel	NNP
en-wikipedia-org-3337	263	133	(	(	-LRB-
en-wikipedia-org-3337	263	134	12	12	CD
en-wikipedia-org-3337	263	135	Jul	jul	NN
en-wikipedia-org-3337	263	136	1994	1994	CD
en-wikipedia-org-3337	263	137	)	)	-RRB-
en-wikipedia-org-3337	263	138	.	.	.
en-wikipedia-org-3337	264	1	A	a	DT
en-wikipedia-org-3337	264	2	Course	course	NN
en-wikipedia-org-3337	264	3	in	in	IN
en-wikipedia-org-3337	264	4	Game	Game	NNP
en-wikipedia-org-3337	264	5	Theory	Theory	NNP
en-wikipedia-org-3337	264	6	.	.	.
en-wikipedia-org-3337	265	1	Cambridge	Cambridge	NNP
en-wikipedia-org-3337	265	2	,	,	,
en-wikipedia-org-3337	265	3	MA	MA	NNP
en-wikipedia-org-3337	265	4	:	:	:
en-wikipedia-org-3337	265	5	MIT	MIT	NNP
en-wikipedia-org-3337	265	6	.	.	.
en-wikipedia-org-3337	266	1	p.	p.	NN
en-wikipedia-org-3337	266	2	 	  	_SP
en-wikipedia-org-3337	266	3	14	14	CD
en-wikipedia-org-3337	266	4	.	.	.
en-wikipedia-org-3337	267	1	ISBN	ISBN	NNP
en-wikipedia-org-3337	267	2	 	  	_SP
en-wikipedia-org-3337	267	3	9780262150415	9780262150415	CD
en-wikipedia-org-3337	267	4	.	.	.
en-wikipedia-org-3337	268	1	^	^	NNP
en-wikipedia-org-3337	268	2	Kreps	Kreps	NNP
en-wikipedia-org-3337	268	3	D.M.	D.M.	NNP
en-wikipedia-org-3337	269	1	(	(	-LRB-
en-wikipedia-org-3337	269	2	1987	1987	CD
en-wikipedia-org-3337	269	3	)	)	-RRB-
en-wikipedia-org-3337	269	4	Nash	Nash	NNP
en-wikipedia-org-3337	269	5	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	269	6	.	.	.
en-wikipedia-org-3337	270	1	In	in	IN
en-wikipedia-org-3337	270	2	:	:	:
en-wikipedia-org-3337	270	3	Palgrave	Palgrave	NNP
en-wikipedia-org-3337	270	4	Macmillan	Macmillan	NNP
en-wikipedia-org-3337	270	5	(	(	-LRB-
en-wikipedia-org-3337	270	6	eds	eds	VB
en-wikipedia-org-3337	270	7	)	)	-RRB-
en-wikipedia-org-3337	270	8	The	the	DT
en-wikipedia-org-3337	270	9	New	New	NNP
en-wikipedia-org-3337	270	10	Palgrave	Palgrave	NNP
en-wikipedia-org-3337	270	11	Dictionary	Dictionary	NNP
en-wikipedia-org-3337	270	12	of	of	IN
en-wikipedia-org-3337	270	13	Economics	Economics	NNP
en-wikipedia-org-3337	270	14	.	.	.
en-wikipedia-org-3337	271	1	Palgrave	Palgrave	NNP
en-wikipedia-org-3337	271	2	Macmillan	Macmillan	NNP
en-wikipedia-org-3337	271	3	,	,	,
en-wikipedia-org-3337	271	4	London	London	NNP
en-wikipedia-org-3337	271	5	.	.	.
en-wikipedia-org-3337	272	1	^	^	NNP
en-wikipedia-org-3337	272	2	Schelling	Schelling	NNP
en-wikipedia-org-3337	272	3	,	,	,
en-wikipedia-org-3337	272	4	Thomas	Thomas	NNP
en-wikipedia-org-3337	272	5	,	,	,
en-wikipedia-org-3337	272	6	The	the	DT
en-wikipedia-org-3337	272	7	Strategy	Strategy	NNP
en-wikipedia-org-3337	272	8	of	of	IN
en-wikipedia-org-3337	272	9	Conflict	conflict	NN
en-wikipedia-org-3337	272	10	,	,	,
en-wikipedia-org-3337	272	11	copyright	copyright	NN
en-wikipedia-org-3337	272	12	1960	1960	CD
en-wikipedia-org-3337	272	13	,	,	,
en-wikipedia-org-3337	272	14	1980	1980	CD
en-wikipedia-org-3337	272	15	,	,	,
en-wikipedia-org-3337	272	16	Harvard	Harvard	NNP
en-wikipedia-org-3337	272	17	University	University	NNP
en-wikipedia-org-3337	272	18	Press	Press	NNP
en-wikipedia-org-3337	272	19	,	,	,
en-wikipedia-org-3337	272	20	ISBN	ISBN	NNP
en-wikipedia-org-3337	272	21	 	  	_SP
en-wikipedia-org-3337	272	22	0	0	CD
en-wikipedia-org-3337	272	23	-	-	SYM
en-wikipedia-org-3337	272	24	674	674	CD
en-wikipedia-org-3337	272	25	-	-	HYPH
en-wikipedia-org-3337	272	26	84031	84031	CD
en-wikipedia-org-3337	272	27	-	-	SYM
en-wikipedia-org-3337	272	28	3	3	CD
en-wikipedia-org-3337	272	29	.	.	.
en-wikipedia-org-3337	273	1	^	^	NNP
en-wikipedia-org-3337	273	2	De	De	NNP
en-wikipedia-org-3337	273	3	Fraja	Fraja	NNP
en-wikipedia-org-3337	273	4	,	,	,
en-wikipedia-org-3337	273	5	G.	G.	NNP
en-wikipedia-org-3337	273	6	;	;	:
en-wikipedia-org-3337	273	7	Oliveira	Oliveira	NNP
en-wikipedia-org-3337	273	8	,	,	,
en-wikipedia-org-3337	273	9	T.	T.	NNP
en-wikipedia-org-3337	273	10	;	;	:
en-wikipedia-org-3337	273	11	Zanchi	Zanchi	NNP
en-wikipedia-org-3337	273	12	,	,	,
en-wikipedia-org-3337	273	13	L.	L.	NNP
en-wikipedia-org-3337	273	14	(	(	-LRB-
en-wikipedia-org-3337	273	15	2010	2010	CD
en-wikipedia-org-3337	273	16	)	)	-RRB-
en-wikipedia-org-3337	273	17	.	.	.
en-wikipedia-org-3337	274	1	"	"	``
en-wikipedia-org-3337	274	2	Must	Must	MD
en-wikipedia-org-3337	274	3	Try	try	VB
en-wikipedia-org-3337	274	4	Harder	hard	RBR
en-wikipedia-org-3337	274	5	:	:	:
en-wikipedia-org-3337	274	6	Evaluating	evaluate	VBG
en-wikipedia-org-3337	274	7	the	the	DT
en-wikipedia-org-3337	274	8	Role	Role	NNP
en-wikipedia-org-3337	274	9	of	of	IN
en-wikipedia-org-3337	274	10	Effort	Effort	NNP
en-wikipedia-org-3337	274	11	in	in	IN
en-wikipedia-org-3337	274	12	Educational	Educational	NNP
en-wikipedia-org-3337	274	13	Attainment	Attainment	NNP
en-wikipedia-org-3337	274	14	"	"	''
en-wikipedia-org-3337	274	15	.	.	.
en-wikipedia-org-3337	275	1	Review	Review	NNP
en-wikipedia-org-3337	275	2	of	of	IN
en-wikipedia-org-3337	275	3	Economics	Economics	NNP
en-wikipedia-org-3337	275	4	and	and	CC
en-wikipedia-org-3337	275	5	Statistics	Statistics	NNPS
en-wikipedia-org-3337	275	6	.	.	.
en-wikipedia-org-3337	276	1	92	92	CD
en-wikipedia-org-3337	276	2	(	(	-LRB-
en-wikipedia-org-3337	276	3	3	3	CD
en-wikipedia-org-3337	276	4	)	)	-RRB-
en-wikipedia-org-3337	276	5	:	:	:
en-wikipedia-org-3337	276	6	577	577	CD
en-wikipedia-org-3337	276	7	.	.	.
en-wikipedia-org-3337	276	8	doi:10.1162	doi:10.1162	NNP
en-wikipedia-org-3337	276	9	/	/	SYM
en-wikipedia-org-3337	276	10	REST_a_00013	REST_a_00013	NNP
en-wikipedia-org-3337	276	11	.	.	.
en-wikipedia-org-3337	277	1	^	^	NNP
en-wikipedia-org-3337	277	2	Ward	Ward	NNP
en-wikipedia-org-3337	277	3	,	,	,
en-wikipedia-org-3337	277	4	H.	H.	NNP
en-wikipedia-org-3337	277	5	(	(	-LRB-
en-wikipedia-org-3337	277	6	1996	1996	CD
en-wikipedia-org-3337	277	7	)	)	-RRB-
en-wikipedia-org-3337	277	8	.	.	.
en-wikipedia-org-3337	278	1	"	"	``
en-wikipedia-org-3337	278	2	Game	Game	NNP
en-wikipedia-org-3337	278	3	Theory	Theory	NNP
en-wikipedia-org-3337	278	4	and	and	CC
en-wikipedia-org-3337	278	5	the	the	DT
en-wikipedia-org-3337	278	6	Politics	Politics	NNPS
en-wikipedia-org-3337	278	7	of	of	IN
en-wikipedia-org-3337	278	8	Global	Global	NNP
en-wikipedia-org-3337	278	9	Warming	Warming	NNP
en-wikipedia-org-3337	278	10	:	:	:
en-wikipedia-org-3337	278	11	The	the	DT
en-wikipedia-org-3337	278	12	State	State	NNP
en-wikipedia-org-3337	278	13	of	of	IN
en-wikipedia-org-3337	278	14	Play	Play	NNP
en-wikipedia-org-3337	278	15	and	and	CC
en-wikipedia-org-3337	278	16	Beyond	beyond	IN
en-wikipedia-org-3337	278	17	"	"	''
en-wikipedia-org-3337	278	18	.	.	.
en-wikipedia-org-3337	279	1	Political	Political	NNP
en-wikipedia-org-3337	279	2	Studies	Studies	NNPS
en-wikipedia-org-3337	279	3	.	.	.
en-wikipedia-org-3337	280	1	44	44	CD
en-wikipedia-org-3337	280	2	(	(	-LRB-
en-wikipedia-org-3337	280	3	5	5	CD
en-wikipedia-org-3337	280	4	)	)	-RRB-
en-wikipedia-org-3337	280	5	:	:	:
en-wikipedia-org-3337	280	6	850–871	850–871	CD
en-wikipedia-org-3337	280	7	.	.	.
en-wikipedia-org-3337	281	1	doi:10.1111	doi:10.1111	NNP
en-wikipedia-org-3337	281	2	/	/	SYM
en-wikipedia-org-3337	281	3	j.1467	j.1467	NNP
en-wikipedia-org-3337	281	4	-	-	HYPH
en-wikipedia-org-3337	281	5	9248.1996.tb00338.x	9248.1996.tb00338.x	NNP
en-wikipedia-org-3337	281	6	.	.	.
en-wikipedia-org-3337	282	1	,	,	,
en-wikipedia-org-3337	282	2	^	^	NNP
en-wikipedia-org-3337	282	3	Thorpe	Thorpe	NNP
en-wikipedia-org-3337	282	4	,	,	,
en-wikipedia-org-3337	282	5	Robert	Robert	NNP
en-wikipedia-org-3337	282	6	B.	B.	NNP
en-wikipedia-org-3337	282	7	;	;	:
en-wikipedia-org-3337	282	8	Jennings	Jennings	NNP
en-wikipedia-org-3337	282	9	,	,	,
en-wikipedia-org-3337	282	10	Simon	Simon	NNP
en-wikipedia-org-3337	282	11	;	;	:
en-wikipedia-org-3337	282	12	Dolder	Dolder	NNP
en-wikipedia-org-3337	282	13	,	,	,
en-wikipedia-org-3337	282	14	Paul	Paul	NNP
en-wikipedia-org-3337	282	15	J.	J.	NNP
en-wikipedia-org-3337	283	1	(	(	-LRB-
en-wikipedia-org-3337	283	2	2017	2017	CD
en-wikipedia-org-3337	283	3	)	)	-RRB-
en-wikipedia-org-3337	283	4	.	.	.
en-wikipedia-org-3337	284	1	"	"	``
en-wikipedia-org-3337	284	2	Risks	risk	NNS
en-wikipedia-org-3337	284	3	and	and	CC
en-wikipedia-org-3337	284	4	benefits	benefit	NNS
en-wikipedia-org-3337	284	5	of	of	IN
en-wikipedia-org-3337	284	6	catching	catch	VBG
en-wikipedia-org-3337	284	7	pretty	pretty	RB
en-wikipedia-org-3337	284	8	good	good	JJ
en-wikipedia-org-3337	284	9	yield	yield	NN
en-wikipedia-org-3337	284	10	in	in	IN
en-wikipedia-org-3337	284	11	multispecies	multispecie	NNS
en-wikipedia-org-3337	284	12	mixed	mixed	JJ
en-wikipedia-org-3337	284	13	fisheries	fishery	NNS
en-wikipedia-org-3337	284	14	"	"	''
en-wikipedia-org-3337	284	15	.	.	.
en-wikipedia-org-3337	285	1	ICES	ICES	NNP
en-wikipedia-org-3337	285	2	Journal	Journal	NNP
en-wikipedia-org-3337	285	3	of	of	IN
en-wikipedia-org-3337	285	4	Marine	Marine	NNP
en-wikipedia-org-3337	285	5	Science	Science	NNP
en-wikipedia-org-3337	285	6	.	.	.
en-wikipedia-org-3337	286	1	74	74	CD
en-wikipedia-org-3337	286	2	(	(	-LRB-
en-wikipedia-org-3337	286	3	8)	8)	CD
en-wikipedia-org-3337	286	4	:	:	SYM
en-wikipedia-org-3337	286	5	2097–2106	2097–2106	CD
en-wikipedia-org-3337	286	6	.	.	.
en-wikipedia-org-3337	287	1	doi:10.1093	doi:10.1093	NNP
en-wikipedia-org-3337	287	2	/	/	SYM
en-wikipedia-org-3337	287	3	icesjms	icesjms	NNP
en-wikipedia-org-3337	287	4	/	/	SYM
en-wikipedia-org-3337	287	5	fsx062	fsx062	-RRB-
en-wikipedia-org-3337	287	6	.	.	.
en-wikipedia-org-3337	288	1	,	,	,
en-wikipedia-org-3337	288	2	^	^	FW
en-wikipedia-org-3337	288	3	"	"	``
en-wikipedia-org-3337	288	4	Marketing	marketing	NN
en-wikipedia-org-3337	288	5	Lessons	lesson	NNS
en-wikipedia-org-3337	288	6	from	from	IN
en-wikipedia-org-3337	288	7	Dr.	Dr.	NNP
en-wikipedia-org-3337	288	8	Nash	Nash	NNP
en-wikipedia-org-3337	288	9	-	-	HYPH
en-wikipedia-org-3337	288	10	Andrew	Andrew	NNP
en-wikipedia-org-3337	288	11	Frank	Frank	NNP
en-wikipedia-org-3337	288	12	"	"	''
en-wikipedia-org-3337	288	13	.	.	.
en-wikipedia-org-3337	289	1	2015	2015	CD
en-wikipedia-org-3337	289	2	-	-	SYM
en-wikipedia-org-3337	289	3	05	05	CD
en-wikipedia-org-3337	289	4	-	-	SYM
en-wikipedia-org-3337	289	5	25	25	CD
en-wikipedia-org-3337	289	6	.	.	.
en-wikipedia-org-3337	290	1	Retrieved	retrieve	VBN
en-wikipedia-org-3337	290	2	2015	2015	CD
en-wikipedia-org-3337	290	3	-	-	SYM
en-wikipedia-org-3337	290	4	08	08	CD
en-wikipedia-org-3337	290	5	-	-	SYM
en-wikipedia-org-3337	290	6	30	30	CD
en-wikipedia-org-3337	290	7	.	.	.
en-wikipedia-org-3337	291	1	^	^	NNP
en-wikipedia-org-3337	291	2	Chiappori	Chiappori	NNP
en-wikipedia-org-3337	291	3	,	,	,
en-wikipedia-org-3337	291	4	P.	P.	NNP
en-wikipedia-org-3337	291	5	-A.	-a.	NN
en-wikipedia-org-3337	291	6	;	;	:
en-wikipedia-org-3337	291	7	Levitt	Levitt	NNP
en-wikipedia-org-3337	291	8	,	,	,
en-wikipedia-org-3337	291	9	S.	S.	NNP
en-wikipedia-org-3337	291	10	;	;	:
en-wikipedia-org-3337	291	11	Groseclose	Groseclose	NNP
en-wikipedia-org-3337	291	12	,	,	,
en-wikipedia-org-3337	291	13	T.	t.	NN
en-wikipedia-org-3337	291	14	(	(	-LRB-
en-wikipedia-org-3337	291	15	2002	2002	CD
en-wikipedia-org-3337	291	16	)	)	-RRB-
en-wikipedia-org-3337	291	17	.	.	.
en-wikipedia-org-3337	292	1	"	"	``
en-wikipedia-org-3337	292	2	Testing	Testing	NNP
en-wikipedia-org-3337	292	3	Mixed	Mixed	NNP
en-wikipedia-org-3337	292	4	-	-	HYPH
en-wikipedia-org-3337	292	5	Strategy	Strategy	NNP
en-wikipedia-org-3337	292	6	Equilibria	Equilibria	NNP
en-wikipedia-org-3337	292	7	when	when	WRB
en-wikipedia-org-3337	292	8	Players	player	NNS
en-wikipedia-org-3337	292	9	Are	be	VBP
en-wikipedia-org-3337	292	10	Heterogeneous	heterogeneous	JJ
en-wikipedia-org-3337	292	11	:	:	:
en-wikipedia-org-3337	292	12	The	the	DT
en-wikipedia-org-3337	292	13	Case	Case	NNP
en-wikipedia-org-3337	292	14	of	of	IN
en-wikipedia-org-3337	292	15	Penalty	Penalty	NNP
en-wikipedia-org-3337	292	16	Kicks	Kicks	NNPS
en-wikipedia-org-3337	292	17	in	in	IN
en-wikipedia-org-3337	292	18	Soccer	Soccer	NNP
en-wikipedia-org-3337	292	19	"	"	''
en-wikipedia-org-3337	292	20	(	(	-LRB-
en-wikipedia-org-3337	292	21	PDF	PDF	NNP
en-wikipedia-org-3337	292	22	)	)	-RRB-
en-wikipedia-org-3337	292	23	.	.	.
en-wikipedia-org-3337	293	1	American	American	NNP
en-wikipedia-org-3337	293	2	Economic	Economic	NNP
en-wikipedia-org-3337	293	3	Review	Review	NNP
en-wikipedia-org-3337	293	4	.	.	.
en-wikipedia-org-3337	294	1	92	92	CD
en-wikipedia-org-3337	294	2	(	(	-LRB-
en-wikipedia-org-3337	294	3	4	4	CD
en-wikipedia-org-3337	294	4	)	)	-RRB-
en-wikipedia-org-3337	294	5	:	:	:
en-wikipedia-org-3337	294	6	1138	1138	CD
en-wikipedia-org-3337	294	7	.	.	.
en-wikipedia-org-3337	295	1	CiteSeerX	CiteSeerX	NNS
en-wikipedia-org-3337	295	2	 	  	_SP
en-wikipedia-org-3337	295	3	10.1.1.178.1646	10.1.1.178.1646	CD
en-wikipedia-org-3337	295	4	.	.	.
en-wikipedia-org-3337	295	5	doi:10.1257/00028280260344678	doi:10.1257/00028280260344678	NNP
en-wikipedia-org-3337	295	6	.	.	.
en-wikipedia-org-3337	296	1	^	^	NNP
en-wikipedia-org-3337	296	2	Djehiche	Djehiche	NNP
en-wikipedia-org-3337	296	3	,	,	,
en-wikipedia-org-3337	296	4	B.	B.	NNP
en-wikipedia-org-3337	296	5	;	;	:
en-wikipedia-org-3337	296	6	Tcheukam	Tcheukam	NNP
en-wikipedia-org-3337	296	7	,	,	,
en-wikipedia-org-3337	296	8	A.	a.	NN
en-wikipedia-org-3337	296	9	;	;	:
en-wikipedia-org-3337	296	10	Tembine	Tembine	NNP
en-wikipedia-org-3337	296	11	,	,	,
en-wikipedia-org-3337	296	12	H.	H.	NNP
en-wikipedia-org-3337	296	13	(	(	-LRB-
en-wikipedia-org-3337	296	14	2017	2017	CD
en-wikipedia-org-3337	296	15	)	)	-RRB-
en-wikipedia-org-3337	296	16	.	.	.
en-wikipedia-org-3337	297	1	"	"	``
en-wikipedia-org-3337	297	2	A	a	DT
en-wikipedia-org-3337	297	3	Mean	Mean	NNP
en-wikipedia-org-3337	297	4	-	-	HYPH
en-wikipedia-org-3337	297	5	Field	Field	NNP
en-wikipedia-org-3337	297	6	Game	Game	NNP
en-wikipedia-org-3337	297	7	of	of	IN
en-wikipedia-org-3337	297	8	Evacuation	Evacuation	NNP
en-wikipedia-org-3337	297	9	in	in	IN
en-wikipedia-org-3337	297	10	Multilevel	Multilevel	NNP
en-wikipedia-org-3337	297	11	Building	Building	NNP
en-wikipedia-org-3337	297	12	"	"	''
en-wikipedia-org-3337	297	13	.	.	.
en-wikipedia-org-3337	298	1	IEEE	IEEE	NNP
en-wikipedia-org-3337	298	2	Transactions	transaction	NNS
en-wikipedia-org-3337	298	3	on	on	IN
en-wikipedia-org-3337	298	4	Automatic	Automatic	NNP
en-wikipedia-org-3337	298	5	Control	Control	NNP
en-wikipedia-org-3337	298	6	.	.	.
en-wikipedia-org-3337	299	1	62	62	CD
en-wikipedia-org-3337	299	2	(	(	-LRB-
en-wikipedia-org-3337	299	3	10	10	CD
en-wikipedia-org-3337	299	4	)	)	-RRB-
en-wikipedia-org-3337	299	5	:	:	:
en-wikipedia-org-3337	299	6	5154–5169	5154–5169	CD
en-wikipedia-org-3337	299	7	.	.	.
en-wikipedia-org-3337	300	1	doi:10.1109	doi:10.1109	NNP
en-wikipedia-org-3337	300	2	/	/	SYM
en-wikipedia-org-3337	300	3	TAC.2017.2679487	TAC.2017.2679487	NNP
en-wikipedia-org-3337	300	4	.	.	.
en-wikipedia-org-3337	301	1	ISSN	issn	NN
en-wikipedia-org-3337	301	2	 	  	_SP
en-wikipedia-org-3337	301	3	0018	0018	CD
en-wikipedia-org-3337	301	4	-	-	SYM
en-wikipedia-org-3337	301	5	9286	9286	CD
en-wikipedia-org-3337	301	6	.	.	.
en-wikipedia-org-3337	302	1	^	^	NNP
en-wikipedia-org-3337	302	2	Djehiche	Djehiche	NNP
en-wikipedia-org-3337	302	3	,	,	,
en-wikipedia-org-3337	302	4	Boualem	Boualem	NNP
en-wikipedia-org-3337	302	5	;	;	:
en-wikipedia-org-3337	302	6	Tcheukam	Tcheukam	NNP
en-wikipedia-org-3337	302	7	,	,	,
en-wikipedia-org-3337	302	8	Alain	Alain	NNP
en-wikipedia-org-3337	302	9	;	;	:
en-wikipedia-org-3337	302	10	Tembine	Tembine	NNP
en-wikipedia-org-3337	302	11	,	,	,
en-wikipedia-org-3337	302	12	Hamidou	Hamidou	NNP
en-wikipedia-org-3337	302	13	(	(	-LRB-
en-wikipedia-org-3337	302	14	2017	2017	CD
en-wikipedia-org-3337	302	15	-	-	SYM
en-wikipedia-org-3337	302	16	09	09	CD
en-wikipedia-org-3337	302	17	-	-	HYPH
en-wikipedia-org-3337	302	18	27	27	CD
en-wikipedia-org-3337	302	19	)	)	-RRB-
en-wikipedia-org-3337	302	20	.	.	.
en-wikipedia-org-3337	303	1	"	"	``
en-wikipedia-org-3337	303	2	Mean	Mean	NNP
en-wikipedia-org-3337	303	3	-	-	HYPH
en-wikipedia-org-3337	303	4	Field	Field	NNP
en-wikipedia-org-3337	303	5	-	-	HYPH
en-wikipedia-org-3337	303	6	Type	Type	NNP
en-wikipedia-org-3337	303	7	Games	Games	NNPS
en-wikipedia-org-3337	303	8	in	in	IN
en-wikipedia-org-3337	303	9	Engineering	Engineering	NNP
en-wikipedia-org-3337	303	10	"	"	''
en-wikipedia-org-3337	303	11	.	.	.
en-wikipedia-org-3337	304	1	AIMS	AIMS	NNP
en-wikipedia-org-3337	304	2	Electronics	Electronics	NNPS
en-wikipedia-org-3337	304	3	and	and	CC
en-wikipedia-org-3337	304	4	Electrical	Electrical	NNP
en-wikipedia-org-3337	304	5	Engineering	Engineering	NNP
en-wikipedia-org-3337	304	6	.	.	.
en-wikipedia-org-3337	305	1	1	1	CD
en-wikipedia-org-3337	305	2	:	:	:
en-wikipedia-org-3337	305	3	18–73	18–73	CD
en-wikipedia-org-3337	305	4	.	.	.
en-wikipedia-org-3337	306	1	arXiv:1605.03281	arXiv:1605.03281	NNP
en-wikipedia-org-3337	306	2	.	.	.
en-wikipedia-org-3337	306	3	doi:10.3934	doi:10.3934	NNP
en-wikipedia-org-3337	306	4	/	/	SYM
en-wikipedia-org-3337	306	5	ElectrEng.2017.1.18	ElectrEng.2017.1.18	NNP
en-wikipedia-org-3337	306	6	.	.	.
en-wikipedia-org-3337	307	1	^	^	NNP
en-wikipedia-org-3337	307	2	Cournot	Cournot	NNP
en-wikipedia-org-3337	307	3	A.	A.	NNP
en-wikipedia-org-3337	308	1	(	(	-LRB-
en-wikipedia-org-3337	308	2	1838	1838	CD
en-wikipedia-org-3337	308	3	)	)	-RRB-
en-wikipedia-org-3337	308	4	Researches	research	NNS
en-wikipedia-org-3337	308	5	on	on	IN
en-wikipedia-org-3337	308	6	the	the	DT
en-wikipedia-org-3337	308	7	Mathematical	Mathematical	NNP
en-wikipedia-org-3337	308	8	Principles	Principles	NNPS
en-wikipedia-org-3337	308	9	of	of	IN
en-wikipedia-org-3337	308	10	the	the	DT
en-wikipedia-org-3337	308	11	Theory	Theory	NNP
en-wikipedia-org-3337	308	12	of	of	IN
en-wikipedia-org-3337	308	13	Wealth	Wealth	NNP
en-wikipedia-org-3337	308	14	^	^	.
en-wikipedia-org-3337	308	15	J.	J.	NNP
en-wikipedia-org-3337	309	1	Von	Von	NNP
en-wikipedia-org-3337	309	2	Neumann	Neumann	NNP
en-wikipedia-org-3337	309	3	,	,	,
en-wikipedia-org-3337	309	4	O.	O.	NNP
en-wikipedia-org-3337	309	5	Morgenstern	Morgenstern	NNP
en-wikipedia-org-3337	309	6	,	,	,
en-wikipedia-org-3337	309	7	Theory	Theory	NNP
en-wikipedia-org-3337	309	8	of	of	IN
en-wikipedia-org-3337	309	9	Games	Games	NNPS
en-wikipedia-org-3337	309	10	and	and	CC
en-wikipedia-org-3337	309	11	Economic	Economic	NNP
en-wikipedia-org-3337	309	12	Behavior	Behavior	NNP
en-wikipedia-org-3337	309	13	,	,	,
en-wikipedia-org-3337	309	14	copyright	copyright	NN
en-wikipedia-org-3337	309	15	1944	1944	CD
en-wikipedia-org-3337	309	16	,	,	,
en-wikipedia-org-3337	309	17	1953	1953	CD
en-wikipedia-org-3337	309	18	,	,	,
en-wikipedia-org-3337	309	19	Princeton	Princeton	NNP
en-wikipedia-org-3337	309	20	University	University	NNP
en-wikipedia-org-3337	309	21	Press	Press	NNP
en-wikipedia-org-3337	309	22	^	^	.
en-wikipedia-org-3337	309	23	Carmona	Carmona	NNP
en-wikipedia-org-3337	309	24	,	,	,
en-wikipedia-org-3337	309	25	Guilherme	Guilherme	NNP
en-wikipedia-org-3337	309	26	;	;	:
en-wikipedia-org-3337	309	27	Podczeck	Podczeck	NNP
en-wikipedia-org-3337	309	28	,	,	,
en-wikipedia-org-3337	309	29	Konrad	Konrad	NNP
en-wikipedia-org-3337	309	30	(	(	-LRB-
en-wikipedia-org-3337	309	31	2009	2009	CD
en-wikipedia-org-3337	309	32	)	)	-RRB-
en-wikipedia-org-3337	309	33	.	.	.
en-wikipedia-org-3337	310	1	"	"	``
en-wikipedia-org-3337	310	2	On	on	IN
en-wikipedia-org-3337	310	3	the	the	DT
en-wikipedia-org-3337	310	4	Existence	Existence	NNP
en-wikipedia-org-3337	310	5	of	of	IN
en-wikipedia-org-3337	310	6	Pure	Pure	NNP
en-wikipedia-org-3337	310	7	Strategy	Strategy	NNP
en-wikipedia-org-3337	310	8	Nash	Nash	NNP
en-wikipedia-org-3337	310	9	Equilibria	Equilibria	NNP
en-wikipedia-org-3337	310	10	in	in	IN
en-wikipedia-org-3337	310	11	Large	Large	NNP
en-wikipedia-org-3337	310	12	Games	Games	NNPS
en-wikipedia-org-3337	310	13	"	"	''
en-wikipedia-org-3337	310	14	(	(	-LRB-
en-wikipedia-org-3337	310	15	PDF	PDF	NNP
en-wikipedia-org-3337	310	16	)	)	-RRB-
en-wikipedia-org-3337	310	17	.	.	.
en-wikipedia-org-3337	311	1	Journal	Journal	NNP
en-wikipedia-org-3337	311	2	of	of	IN
en-wikipedia-org-3337	311	3	Economic	Economic	NNP
en-wikipedia-org-3337	311	4	Theory	Theory	NNP
en-wikipedia-org-3337	311	5	.	.	.
en-wikipedia-org-3337	312	1	144	144	CD
en-wikipedia-org-3337	312	2	(	(	-LRB-
en-wikipedia-org-3337	312	3	3	3	CD
en-wikipedia-org-3337	312	4	)	)	-RRB-
en-wikipedia-org-3337	312	5	:	:	:
en-wikipedia-org-3337	312	6	1300–1319	1300–1319	CD
en-wikipedia-org-3337	312	7	.	.	.
en-wikipedia-org-3337	313	1	doi:10.1016	doi:10.1016	NNP
en-wikipedia-org-3337	313	2	/	/	SYM
en-wikipedia-org-3337	313	3	j.jet.2008.11.009	j.jet.2008.11.009	JJ
en-wikipedia-org-3337	313	4	.	.	.
en-wikipedia-org-3337	314	1	SSRN	SSRN	NNP
en-wikipedia-org-3337	314	2	 	  	_SP
en-wikipedia-org-3337	314	3	882466	882466	CD
en-wikipedia-org-3337	314	4	.	.	.
en-wikipedia-org-3337	315	1	^	^	NNP
en-wikipedia-org-3337	315	2	a	a	DT
en-wikipedia-org-3337	315	3	b	b	NN
en-wikipedia-org-3337	315	4	von	von	NNP
en-wikipedia-org-3337	315	5	Ahn	Ahn	NNP
en-wikipedia-org-3337	315	6	,	,	,
en-wikipedia-org-3337	315	7	Luis	Luis	NNP
en-wikipedia-org-3337	315	8	.	.	.
en-wikipedia-org-3337	316	1	"	"	``
en-wikipedia-org-3337	316	2	Preliminaries	preliminary	NNS
en-wikipedia-org-3337	316	3	of	of	IN
en-wikipedia-org-3337	316	4	Game	Game	NNP
en-wikipedia-org-3337	316	5	Theory	Theory	NNP
en-wikipedia-org-3337	316	6	"	"	''
en-wikipedia-org-3337	316	7	(	(	-LRB-
en-wikipedia-org-3337	316	8	PDF	PDF	NNP
en-wikipedia-org-3337	316	9	)	)	-RRB-
en-wikipedia-org-3337	316	10	.	.	.
en-wikipedia-org-3337	317	1	Archived	archived	JJ
en-wikipedia-org-3337	317	2	from	from	IN
en-wikipedia-org-3337	317	3	the	the	DT
en-wikipedia-org-3337	317	4	original	original	JJ
en-wikipedia-org-3337	317	5	(	(	-LRB-
en-wikipedia-org-3337	317	6	PDF	PDF	NNP
en-wikipedia-org-3337	317	7	)	)	-RRB-
en-wikipedia-org-3337	317	8	on	on	IN
en-wikipedia-org-3337	317	9	2011	2011	CD
en-wikipedia-org-3337	317	10	-	-	SYM
en-wikipedia-org-3337	317	11	10	10	CD
en-wikipedia-org-3337	317	12	-	-	SYM
en-wikipedia-org-3337	317	13	18	18	CD
en-wikipedia-org-3337	317	14	.	.	.
en-wikipedia-org-3337	318	1	Retrieved	retrieve	VBN
en-wikipedia-org-3337	318	2	2008	2008	CD
en-wikipedia-org-3337	318	3	-	-	SYM
en-wikipedia-org-3337	318	4	11	11	CD
en-wikipedia-org-3337	318	5	-	-	SYM
en-wikipedia-org-3337	318	6	07	07	CD
en-wikipedia-org-3337	318	7	.	.	.
en-wikipedia-org-3337	319	1	^	^	FW
en-wikipedia-org-3337	319	2	"	"	``
en-wikipedia-org-3337	319	3	Nash	Nash	NNP
en-wikipedia-org-3337	319	4	Equilibria	Equilibria	NNP
en-wikipedia-org-3337	319	5	"	"	''
en-wikipedia-org-3337	319	6	.	.	.
en-wikipedia-org-3337	320	1	hoylab.cornell.edu	hoylab.cornell.edu	NNS
en-wikipedia-org-3337	320	2	.	.	.
en-wikipedia-org-3337	321	1	Retrieved	Retrieved	NNP
en-wikipedia-org-3337	321	2	2019	2019	CD
en-wikipedia-org-3337	321	3	-	-	SYM
en-wikipedia-org-3337	321	4	12	12	CD
en-wikipedia-org-3337	321	5	-	-	HYPH
en-wikipedia-org-3337	321	6	08	08	CD
en-wikipedia-org-3337	321	7	.	.	.
en-wikipedia-org-3337	322	1	^	^	NNP
en-wikipedia-org-3337	322	2	MIT	MIT	NNP
en-wikipedia-org-3337	322	3	OpenCourseWare	OpenCourseWare	NNP
en-wikipedia-org-3337	322	4	.	.	.
en-wikipedia-org-3337	323	1	6.254	6.254	CD
en-wikipedia-org-3337	323	2	:	:	:
en-wikipedia-org-3337	323	3	Game	Game	NNP
en-wikipedia-org-3337	323	4	Theory	Theory	NNP
en-wikipedia-org-3337	323	5	with	with	IN
en-wikipedia-org-3337	323	6	Engineering	Engineering	NNP
en-wikipedia-org-3337	323	7	Applications	Applications	NNPS
en-wikipedia-org-3337	323	8	,	,	,
en-wikipedia-org-3337	323	9	Spring	Spring	NNP
en-wikipedia-org-3337	323	10	2010	2010	CD
en-wikipedia-org-3337	323	11	.	.	.
en-wikipedia-org-3337	324	1	Lecture	lecture	NN
en-wikipedia-org-3337	324	2	6	6	CD
en-wikipedia-org-3337	324	3	:	:	:
en-wikipedia-org-3337	324	4	Continuous	continuous	JJ
en-wikipedia-org-3337	324	5	and	and	CC
en-wikipedia-org-3337	324	6	Discontinuous	Discontinuous	NNP
en-wikipedia-org-3337	324	7	Games	Games	NNPS
en-wikipedia-org-3337	324	8	.	.	.
en-wikipedia-org-3337	325	1	^	^	NNP
en-wikipedia-org-3337	325	2	a	a	DT
en-wikipedia-org-3337	325	3	b	b	NNP
en-wikipedia-org-3337	325	4	B.	B.	NNP
en-wikipedia-org-3337	325	5	D.	D.	NNP
en-wikipedia-org-3337	325	6	Bernheim	Bernheim	NNP
en-wikipedia-org-3337	325	7	;	;	:
en-wikipedia-org-3337	325	8	B.	B.	NNP
en-wikipedia-org-3337	325	9	Peleg	Peleg	NNP
en-wikipedia-org-3337	325	10	;	;	:
en-wikipedia-org-3337	325	11	M.	M.	NNP
en-wikipedia-org-3337	325	12	D.	D.	NNP
en-wikipedia-org-3337	325	13	Whinston	Whinston	NNP
en-wikipedia-org-3337	325	14	(	(	-LRB-
en-wikipedia-org-3337	325	15	1987	1987	CD
en-wikipedia-org-3337	325	16	)	)	-RRB-
en-wikipedia-org-3337	325	17	,	,	,
en-wikipedia-org-3337	325	18	"	"	``
en-wikipedia-org-3337	325	19	Coalition	Coalition	NNP
en-wikipedia-org-3337	325	20	-	-	HYPH
en-wikipedia-org-3337	325	21	Proof	Proof	NNP
en-wikipedia-org-3337	325	22	Equilibria	Equilibria	NNP
en-wikipedia-org-3337	325	23	I.	I.	NNP
en-wikipedia-org-3337	325	24	Concepts	Concepts	NNP
en-wikipedia-org-3337	325	25	"	"	''
en-wikipedia-org-3337	325	26	,	,	,
en-wikipedia-org-3337	325	27	Journal	Journal	NNP
en-wikipedia-org-3337	325	28	of	of	IN
en-wikipedia-org-3337	325	29	Economic	Economic	NNP
en-wikipedia-org-3337	325	30	Theory	Theory	NNP
en-wikipedia-org-3337	325	31	,	,	,
en-wikipedia-org-3337	325	32	42	42	CD
en-wikipedia-org-3337	325	33	(	(	-LRB-
en-wikipedia-org-3337	325	34	1	1	CD
en-wikipedia-org-3337	325	35	)	)	-RRB-
en-wikipedia-org-3337	325	36	:	:	:
en-wikipedia-org-3337	325	37	1–12	1–12	CD
en-wikipedia-org-3337	325	38	,	,	,
en-wikipedia-org-3337	325	39	doi:10.1016/0022	doi:10.1016/0022	FW
en-wikipedia-org-3337	325	40	-	-	HYPH
en-wikipedia-org-3337	325	41	0531(87)90099	0531(87)90099	NNP
en-wikipedia-org-3337	325	42	-	-	HYPH
en-wikipedia-org-3337	325	43	8	8	CD
en-wikipedia-org-3337	325	44	.	.	.
en-wikipedia-org-3337	326	1	^	^	NNP
en-wikipedia-org-3337	326	2	Aumann	Aumann	NNP
en-wikipedia-org-3337	326	3	,	,	,
en-wikipedia-org-3337	326	4	R.	R.	NNP
en-wikipedia-org-3337	326	5	(	(	-LRB-
en-wikipedia-org-3337	326	6	1959	1959	CD
en-wikipedia-org-3337	326	7	)	)	-RRB-
en-wikipedia-org-3337	326	8	.	.	.
en-wikipedia-org-3337	327	1	"	"	``
en-wikipedia-org-3337	327	2	Acceptable	acceptable	JJ
en-wikipedia-org-3337	327	3	points	point	NNS
en-wikipedia-org-3337	327	4	in	in	IN
en-wikipedia-org-3337	327	5	general	general	JJ
en-wikipedia-org-3337	327	6	cooperative	cooperative	JJ
en-wikipedia-org-3337	327	7	n	n	JJ
en-wikipedia-org-3337	327	8	-	-	HYPH
en-wikipedia-org-3337	327	9	person	person	NN
en-wikipedia-org-3337	327	10	games	game	NNS
en-wikipedia-org-3337	327	11	"	"	''
en-wikipedia-org-3337	327	12	.	.	.
en-wikipedia-org-3337	328	1	Contributions	contribution	NNS
en-wikipedia-org-3337	328	2	to	to	IN
en-wikipedia-org-3337	328	3	the	the	DT
en-wikipedia-org-3337	328	4	Theory	Theory	NNP
en-wikipedia-org-3337	328	5	of	of	IN
en-wikipedia-org-3337	328	6	Games	Games	NNPS
en-wikipedia-org-3337	328	7	.	.	.
en-wikipedia-org-3337	329	1	IV	IV	NNP
en-wikipedia-org-3337	329	2	.	.	.
en-wikipedia-org-3337	330	1	Princeton	Princeton	NNP
en-wikipedia-org-3337	330	2	,	,	,
en-wikipedia-org-3337	330	3	N.J.	New Jersey	NNP
en-wikipedia-org-3337	330	4	:	:	:
en-wikipedia-org-3337	330	5	Princeton	Princeton	NNP
en-wikipedia-org-3337	330	6	University	University	NNP
en-wikipedia-org-3337	330	7	Press	Press	NNP
en-wikipedia-org-3337	330	8	.	.	.
en-wikipedia-org-3337	331	1	ISBN	ISBN	NNP
en-wikipedia-org-3337	331	2	 	  	_SP
en-wikipedia-org-3337	331	3	978	978	CD
en-wikipedia-org-3337	331	4	-	-	HYPH
en-wikipedia-org-3337	331	5	1	1	CD
en-wikipedia-org-3337	331	6	-	-	HYPH
en-wikipedia-org-3337	331	7	4008	4008	CD
en-wikipedia-org-3337	331	8	-	-	HYPH
en-wikipedia-org-3337	331	9	8216	8216	CD
en-wikipedia-org-3337	331	10	-	-	HYPH
en-wikipedia-org-3337	331	11	8	8	CD
en-wikipedia-org-3337	331	12	.	.	.
en-wikipedia-org-3337	332	1	^	^	NNP
en-wikipedia-org-3337	332	2	D.	D.	NNP
en-wikipedia-org-3337	332	3	Moreno	Moreno	NNP
en-wikipedia-org-3337	332	4	;	;	:
en-wikipedia-org-3337	332	5	J.	J.	NNP
en-wikipedia-org-3337	332	6	Wooders	Wooders	NNP
en-wikipedia-org-3337	332	7	(	(	-LRB-
en-wikipedia-org-3337	332	8	1996	1996	CD
en-wikipedia-org-3337	332	9	)	)	-RRB-
en-wikipedia-org-3337	332	10	,	,	,
en-wikipedia-org-3337	332	11	"	"	``
en-wikipedia-org-3337	332	12	Coalition	Coalition	NNP
en-wikipedia-org-3337	332	13	-	-	HYPH
en-wikipedia-org-3337	332	14	Proof	Proof	NNP
en-wikipedia-org-3337	332	15	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	332	16	"	"	''
en-wikipedia-org-3337	332	17	(	(	-LRB-
en-wikipedia-org-3337	332	18	PDF	PDF	NNP
en-wikipedia-org-3337	332	19	)	)	-RRB-
en-wikipedia-org-3337	332	20	,	,	,
en-wikipedia-org-3337	332	21	Games	Games	NNPS
en-wikipedia-org-3337	332	22	and	and	CC
en-wikipedia-org-3337	332	23	Economic	Economic	NNP
en-wikipedia-org-3337	332	24	Behavior	Behavior	NNP
en-wikipedia-org-3337	332	25	,	,	,
en-wikipedia-org-3337	332	26	17	17	CD
en-wikipedia-org-3337	332	27	(	(	-LRB-
en-wikipedia-org-3337	332	28	1	1	CD
en-wikipedia-org-3337	332	29	)	)	-RRB-
en-wikipedia-org-3337	332	30	:	:	:
en-wikipedia-org-3337	332	31	80–112	80–112	NNP
en-wikipedia-org-3337	332	32	,	,	,
en-wikipedia-org-3337	332	33	doi:10.1006	doi:10.1006	NNP
en-wikipedia-org-3337	332	34	/	/	SYM
en-wikipedia-org-3337	332	35	game.1996.0095	game.1996.0095	NNP
en-wikipedia-org-3337	332	36	,	,	,
en-wikipedia-org-3337	332	37	hdl:10016/4408	hdl:10016/4408	NNP
en-wikipedia-org-3337	332	38	.	.	.
en-wikipedia-org-3337	333	1	^	^	NNP
en-wikipedia-org-3337	333	2	T.	T.	NNP
en-wikipedia-org-3337	333	3	L.	L.	NNP
en-wikipedia-org-3337	333	4	Turocy	Turocy	NNP
en-wikipedia-org-3337	333	5	,	,	,
en-wikipedia-org-3337	333	6	B.	B.	NNP
en-wikipedia-org-3337	334	1	Von	Von	NNP
en-wikipedia-org-3337	334	2	Stengel	Stengel	NNP
en-wikipedia-org-3337	334	3	,	,	,
en-wikipedia-org-3337	334	4	Game	Game	NNP
en-wikipedia-org-3337	334	5	Theory	Theory	NNP
en-wikipedia-org-3337	334	6	,	,	,
en-wikipedia-org-3337	334	7	copyright	copyright	NN
en-wikipedia-org-3337	334	8	2001	2001	CD
en-wikipedia-org-3337	334	9	,	,	,
en-wikipedia-org-3337	334	10	Texas	Texas	NNP
en-wikipedia-org-3337	334	11	A&M	A&M	NNP
en-wikipedia-org-3337	334	12	University	University	NNP
en-wikipedia-org-3337	334	13	,	,	,
en-wikipedia-org-3337	334	14	London	London	NNP
en-wikipedia-org-3337	334	15	School	School	NNP
en-wikipedia-org-3337	334	16	of	of	IN
en-wikipedia-org-3337	334	17	Economics	Economics	NNP
en-wikipedia-org-3337	334	18	,	,	,
en-wikipedia-org-3337	334	19	pages	page	VBZ
en-wikipedia-org-3337	334	20	141	141	CD
en-wikipedia-org-3337	334	21	-	-	SYM
en-wikipedia-org-3337	334	22	144	144	CD
en-wikipedia-org-3337	334	23	.	.	.
en-wikipedia-org-3337	335	1	Nash	Nash	NNP
en-wikipedia-org-3337	335	2	proved	prove	VBD
en-wikipedia-org-3337	335	3	that	that	IN
en-wikipedia-org-3337	335	4	a	a	DT
en-wikipedia-org-3337	335	5	perfect	perfect	JJ
en-wikipedia-org-3337	335	6	NE	NE	NNP
en-wikipedia-org-3337	335	7	exists	exist	VBZ
en-wikipedia-org-3337	335	8	for	for	IN
en-wikipedia-org-3337	335	9	this	this	DT
en-wikipedia-org-3337	335	10	type	type	NN
en-wikipedia-org-3337	335	11	of	of	IN
en-wikipedia-org-3337	335	12	finite	finite	JJ
en-wikipedia-org-3337	335	13	extensive	extensive	JJ
en-wikipedia-org-3337	335	14	form	form	NN
en-wikipedia-org-3337	335	15	game[citation	game[citation	NN
en-wikipedia-org-3337	335	16	needed	need	VBN
en-wikipedia-org-3337	335	17	]	]	-RRB-
en-wikipedia-org-3337	335	18	–	–	:
en-wikipedia-org-3337	335	19	it	-PRON-	PRP
en-wikipedia-org-3337	335	20	can	can	MD
en-wikipedia-org-3337	335	21	be	be	VB
en-wikipedia-org-3337	335	22	represented	represent	VBN
en-wikipedia-org-3337	335	23	as	as	IN
en-wikipedia-org-3337	335	24	a	a	DT
en-wikipedia-org-3337	335	25	strategy	strategy	NN
en-wikipedia-org-3337	335	26	complying	comply	VBG
en-wikipedia-org-3337	335	27	with	with	IN
en-wikipedia-org-3337	335	28	his	-PRON-	PRP$
en-wikipedia-org-3337	335	29	original	original	JJ
en-wikipedia-org-3337	335	30	conditions	condition	NNS
en-wikipedia-org-3337	335	31	for	for	IN
en-wikipedia-org-3337	335	32	a	a	DT
en-wikipedia-org-3337	335	33	game	game	NN
en-wikipedia-org-3337	335	34	with	with	IN
en-wikipedia-org-3337	335	35	a	a	DT
en-wikipedia-org-3337	335	36	NE	NE	NNP
en-wikipedia-org-3337	335	37	.	.	.
en-wikipedia-org-3337	336	1	Such	such	JJ
en-wikipedia-org-3337	336	2	games	game	NNS
en-wikipedia-org-3337	336	3	may	may	MD
en-wikipedia-org-3337	336	4	not	not	RB
en-wikipedia-org-3337	336	5	have	have	VB
en-wikipedia-org-3337	336	6	unique	unique	JJ
en-wikipedia-org-3337	336	7	NE	NE	NNP
en-wikipedia-org-3337	336	8	,	,	,
en-wikipedia-org-3337	336	9	but	but	CC
en-wikipedia-org-3337	336	10	at	at	RB
en-wikipedia-org-3337	336	11	least	least	JJS
en-wikipedia-org-3337	336	12	one	one	CD
en-wikipedia-org-3337	336	13	of	of	IN
en-wikipedia-org-3337	336	14	the	the	DT
en-wikipedia-org-3337	336	15	many	many	JJ
en-wikipedia-org-3337	336	16	equilibrium	equilibrium	NN
en-wikipedia-org-3337	336	17	strategies	strategy	NNS
en-wikipedia-org-3337	336	18	would	would	MD
en-wikipedia-org-3337	336	19	be	be	VB
en-wikipedia-org-3337	336	20	played	play	VBN
en-wikipedia-org-3337	336	21	by	by	IN
en-wikipedia-org-3337	336	22	hypothetical	hypothetical	JJ
en-wikipedia-org-3337	336	23	players	player	NNS
en-wikipedia-org-3337	336	24	having	have	VBG
en-wikipedia-org-3337	336	25	perfect	perfect	JJ
en-wikipedia-org-3337	336	26	knowledge	knowledge	NN
en-wikipedia-org-3337	336	27	of	of	IN
en-wikipedia-org-3337	336	28	all	all	DT
en-wikipedia-org-3337	336	29	10150	10150	CD
en-wikipedia-org-3337	336	30	game	game	NN
en-wikipedia-org-3337	336	31	trees[citation	trees[citation	,
en-wikipedia-org-3337	336	32	needed	need	VBN
en-wikipedia-org-3337	336	33	]	]	-RRB-
en-wikipedia-org-3337	336	34	.	.	.
en-wikipedia-org-3337	337	1	^	^	NNP
en-wikipedia-org-3337	337	2	J.	J.	NNP
en-wikipedia-org-3337	337	3	C.	C.	NNP
en-wikipedia-org-3337	337	4	Cox	Cox	NNP
en-wikipedia-org-3337	337	5	,	,	,
en-wikipedia-org-3337	337	6	M.	M.	NNP
en-wikipedia-org-3337	337	7	Walker	Walker	NNP
en-wikipedia-org-3337	337	8	,	,	,
en-wikipedia-org-3337	337	9	Learning	learn	VBG
en-wikipedia-org-3337	337	10	to	to	TO
en-wikipedia-org-3337	337	11	Play	play	VB
en-wikipedia-org-3337	337	12	Cournot	Cournot	NNP
en-wikipedia-org-3337	337	13	Duoploy	duoploy	NN
en-wikipedia-org-3337	337	14	Strategies	strategy	NNS
en-wikipedia-org-3337	337	15	Archived	Archived	NNP
en-wikipedia-org-3337	337	16	2013	2013	CD
en-wikipedia-org-3337	337	17	-	-	SYM
en-wikipedia-org-3337	337	18	12	12	CD
en-wikipedia-org-3337	337	19	-	-	SYM
en-wikipedia-org-3337	337	20	11	11	CD
en-wikipedia-org-3337	337	21	at	at	IN
en-wikipedia-org-3337	337	22	the	the	DT
en-wikipedia-org-3337	337	23	Wayback	Wayback	NNP
en-wikipedia-org-3337	337	24	Machine	Machine	NNP
en-wikipedia-org-3337	337	25	,	,	,
en-wikipedia-org-3337	337	26	copyright	copyright	NN
en-wikipedia-org-3337	337	27	1997	1997	CD
en-wikipedia-org-3337	337	28	,	,	,
en-wikipedia-org-3337	337	29	Texas	Texas	NNP
en-wikipedia-org-3337	337	30	A&M	A&M	NNP
en-wikipedia-org-3337	337	31	University	University	NNP
en-wikipedia-org-3337	337	32	,	,	,
en-wikipedia-org-3337	337	33	University	University	NNP
en-wikipedia-org-3337	337	34	of	of	IN
en-wikipedia-org-3337	337	35	Arizona	Arizona	NNP
en-wikipedia-org-3337	337	36	,	,	,
en-wikipedia-org-3337	337	37	pages	page	VBZ
en-wikipedia-org-3337	337	38	141	141	CD
en-wikipedia-org-3337	337	39	-	-	SYM
en-wikipedia-org-3337	337	40	144	144	CD
en-wikipedia-org-3337	337	41	^	^	.
en-wikipedia-org-3337	337	42	Fudenburg	Fudenburg	NNP
en-wikipedia-org-3337	337	43	,	,	,
en-wikipedia-org-3337	337	44	Drew	Drew	NNP
en-wikipedia-org-3337	337	45	;	;	.
en-wikipedia-org-3337	337	46	Tirole	Tirole	NNP
en-wikipedia-org-3337	337	47	,	,	,
en-wikipedia-org-3337	337	48	Jean	Jean	NNP
en-wikipedia-org-3337	337	49	(	(	-LRB-
en-wikipedia-org-3337	337	50	1991	1991	CD
en-wikipedia-org-3337	337	51	)	)	-RRB-
en-wikipedia-org-3337	337	52	.	.	.
en-wikipedia-org-3337	338	1	Game	Game	NNP
en-wikipedia-org-3337	338	2	Theory	Theory	NNP
en-wikipedia-org-3337	338	3	.	.	.
en-wikipedia-org-3337	339	1	MIT	MIT	NNP
en-wikipedia-org-3337	339	2	Press	Press	NNP
en-wikipedia-org-3337	339	3	.	.	.
en-wikipedia-org-3337	340	1	ISBN	ISBN	NNP
en-wikipedia-org-3337	340	2	 	  	_SP
en-wikipedia-org-3337	340	3	978	978	CD
en-wikipedia-org-3337	340	4	-	-	HYPH
en-wikipedia-org-3337	340	5	0	0	CD
en-wikipedia-org-3337	340	6	-	-	HYPH
en-wikipedia-org-3337	340	7	262	262	CD
en-wikipedia-org-3337	340	8	-	-	HYPH
en-wikipedia-org-3337	340	9	06141	06141	CD
en-wikipedia-org-3337	340	10	-	-	HYPH
en-wikipedia-org-3337	340	11	4	4	CD
en-wikipedia-org-3337	340	12	.	.	.
en-wikipedia-org-3337	341	1	References[edit	references[edit	LS
en-wikipedia-org-3337	341	2	]	]	-RRB-
en-wikipedia-org-3337	341	3	Game	game	NN
en-wikipedia-org-3337	341	4	theory	theory	NN
en-wikipedia-org-3337	341	5	textbooks[edit	textbooks[edit	LS
en-wikipedia-org-3337	341	6	]	]	-RRB-
en-wikipedia-org-3337	341	7	Dixit	Dixit	NNP
en-wikipedia-org-3337	341	8	,	,	,
en-wikipedia-org-3337	341	9	Avinash	Avinash	NNP
en-wikipedia-org-3337	341	10	,	,	,
en-wikipedia-org-3337	341	11	Susan	Susan	NNP
en-wikipedia-org-3337	341	12	Skeath	Skeath	NNP
en-wikipedia-org-3337	341	13	and	and	CC
en-wikipedia-org-3337	341	14	David	David	NNP
en-wikipedia-org-3337	341	15	Reiley	Reiley	NNP
en-wikipedia-org-3337	341	16	.	.	.
en-wikipedia-org-3337	342	1	Games	Games	NNPS
en-wikipedia-org-3337	342	2	of	of	IN
en-wikipedia-org-3337	342	3	Strategy	Strategy	NNP
en-wikipedia-org-3337	342	4	.	.	.
en-wikipedia-org-3337	343	1	W.W.	W.W.	NNP
en-wikipedia-org-3337	343	2	Norton	Norton	NNP
en-wikipedia-org-3337	343	3	&	&	CC
en-wikipedia-org-3337	343	4	Company	Company	NNP
en-wikipedia-org-3337	343	5	.	.	.
en-wikipedia-org-3337	344	1	(	(	-LRB-
en-wikipedia-org-3337	344	2	Third	third	JJ
en-wikipedia-org-3337	344	3	edition	edition	NN
en-wikipedia-org-3337	344	4	in	in	IN
en-wikipedia-org-3337	344	5	2009	2009	CD
en-wikipedia-org-3337	344	6	)	)	-RRB-
en-wikipedia-org-3337	344	7	Dutta	Dutta	NNP
en-wikipedia-org-3337	344	8	,	,	,
en-wikipedia-org-3337	344	9	Prajit	Prajit	NNP
en-wikipedia-org-3337	344	10	K.	K.	NNP
en-wikipedia-org-3337	344	11	(	(	-LRB-
en-wikipedia-org-3337	344	12	1999	1999	CD
en-wikipedia-org-3337	344	13	)	)	-RRB-
en-wikipedia-org-3337	344	14	,	,	,
en-wikipedia-org-3337	344	15	Strategies	strategy	NNS
en-wikipedia-org-3337	344	16	and	and	CC
en-wikipedia-org-3337	344	17	games	game	NNS
en-wikipedia-org-3337	344	18	:	:	:
en-wikipedia-org-3337	344	19	theory	theory	NN
en-wikipedia-org-3337	344	20	and	and	CC
en-wikipedia-org-3337	344	21	practice	practice	NN
en-wikipedia-org-3337	344	22	,	,	,
en-wikipedia-org-3337	344	23	MIT	MIT	NNP
en-wikipedia-org-3337	344	24	Press	Press	NNP
en-wikipedia-org-3337	344	25	,	,	,
en-wikipedia-org-3337	344	26	ISBN	ISBN	NNP
en-wikipedia-org-3337	344	27	 	  	_SP
en-wikipedia-org-3337	344	28	978	978	CD
en-wikipedia-org-3337	344	29	-	-	HYPH
en-wikipedia-org-3337	344	30	0	0	CD
en-wikipedia-org-3337	344	31	-	-	HYPH
en-wikipedia-org-3337	344	32	262	262	CD
en-wikipedia-org-3337	344	33	-	-	HYPH
en-wikipedia-org-3337	344	34	04169	04169	CD
en-wikipedia-org-3337	344	35	-	-	HYPH
en-wikipedia-org-3337	344	36	0	0	CD
en-wikipedia-org-3337	344	37	.	.	.
en-wikipedia-org-3337	345	1	Suitable	suitable	JJ
en-wikipedia-org-3337	345	2	for	for	IN
en-wikipedia-org-3337	345	3	undergraduate	undergraduate	NN
en-wikipedia-org-3337	345	4	and	and	CC
en-wikipedia-org-3337	345	5	business	business	NN
en-wikipedia-org-3337	345	6	students	student	NNS
en-wikipedia-org-3337	345	7	.	.	.
en-wikipedia-org-3337	346	1	Fudenberg	Fudenberg	NNP
en-wikipedia-org-3337	346	2	,	,	,
en-wikipedia-org-3337	346	3	Drew	Drew	NNP
en-wikipedia-org-3337	346	4	and	and	CC
en-wikipedia-org-3337	346	5	Jean	Jean	NNP
en-wikipedia-org-3337	346	6	Tirole	Tirole	NNP
en-wikipedia-org-3337	346	7	(	(	-LRB-
en-wikipedia-org-3337	346	8	1991	1991	CD
en-wikipedia-org-3337	346	9	)	)	-RRB-
en-wikipedia-org-3337	346	10	Game	Game	NNP
en-wikipedia-org-3337	346	11	Theory	Theory	NNP
en-wikipedia-org-3337	346	12	MIT	MIT	NNP
en-wikipedia-org-3337	346	13	Press	Press	NNP
en-wikipedia-org-3337	346	14	.	.	.
en-wikipedia-org-3337	347	1	Leyton	Leyton	NNP
en-wikipedia-org-3337	347	2	-	-	HYPH
en-wikipedia-org-3337	347	3	Brown	Brown	NNP
en-wikipedia-org-3337	347	4	,	,	,
en-wikipedia-org-3337	347	5	Kevin	Kevin	NNP
en-wikipedia-org-3337	347	6	;	;	:
en-wikipedia-org-3337	347	7	Shoham	Shoham	NNP
en-wikipedia-org-3337	347	8	,	,	,
en-wikipedia-org-3337	347	9	Yoav	Yoav	NNP
en-wikipedia-org-3337	347	10	(	(	-LRB-
en-wikipedia-org-3337	347	11	2008	2008	CD
en-wikipedia-org-3337	347	12	)	)	-RRB-
en-wikipedia-org-3337	347	13	,	,	,
en-wikipedia-org-3337	347	14	Essentials	Essentials	NNPS
en-wikipedia-org-3337	347	15	of	of	IN
en-wikipedia-org-3337	347	16	Game	Game	NNP
en-wikipedia-org-3337	347	17	Theory	Theory	NNP
en-wikipedia-org-3337	347	18	:	:	:
en-wikipedia-org-3337	347	19	A	a	DT
en-wikipedia-org-3337	347	20	Concise	Concise	NNP
en-wikipedia-org-3337	347	21	,	,	,
en-wikipedia-org-3337	347	22	Multidisciplinary	Multidisciplinary	NNP
en-wikipedia-org-3337	347	23	Introduction	Introduction	NNP
en-wikipedia-org-3337	347	24	,	,	,
en-wikipedia-org-3337	347	25	San	San	NNP
en-wikipedia-org-3337	347	26	Rafael	Rafael	NNP
en-wikipedia-org-3337	347	27	,	,	,
en-wikipedia-org-3337	347	28	CA	CA	NNP
en-wikipedia-org-3337	347	29	:	:	:
en-wikipedia-org-3337	347	30	Morgan	Morgan	NNP
en-wikipedia-org-3337	347	31	&	&	CC
en-wikipedia-org-3337	347	32	Claypool	Claypool	NNP
en-wikipedia-org-3337	347	33	Publishers	Publishers	NNPS
en-wikipedia-org-3337	347	34	,	,	,
en-wikipedia-org-3337	347	35	ISBN	ISBN	NNP
en-wikipedia-org-3337	347	36	 	  	_SP
en-wikipedia-org-3337	347	37	978	978	CD
en-wikipedia-org-3337	347	38	-	-	HYPH
en-wikipedia-org-3337	347	39	1	1	CD
en-wikipedia-org-3337	347	40	-	-	HYPH
en-wikipedia-org-3337	347	41	59829	59829	CD
en-wikipedia-org-3337	347	42	-	-	HYPH
en-wikipedia-org-3337	347	43	593	593	CD
en-wikipedia-org-3337	347	44	-	-	HYPH
en-wikipedia-org-3337	347	45	1	1	CD
en-wikipedia-org-3337	347	46	.	.	.
en-wikipedia-org-3337	348	1	An	an	DT
en-wikipedia-org-3337	348	2	88-page	88-page	CD
en-wikipedia-org-3337	348	3	mathematical	mathematical	JJ
en-wikipedia-org-3337	348	4	introduction	introduction	NN
en-wikipedia-org-3337	348	5	;	;	:
en-wikipedia-org-3337	348	6	see	see	VB
en-wikipedia-org-3337	348	7	Chapter	chapter	NN
en-wikipedia-org-3337	348	8	2	2	CD
en-wikipedia-org-3337	348	9	.	.	.
en-wikipedia-org-3337	349	1	Free	free	JJ
en-wikipedia-org-3337	349	2	online	online	RB
en-wikipedia-org-3337	349	3	at	at	IN
en-wikipedia-org-3337	349	4	many	many	JJ
en-wikipedia-org-3337	349	5	universities	university	NNS
en-wikipedia-org-3337	349	6	.	.	.
en-wikipedia-org-3337	350	1	Morgenstern	Morgenstern	NNP
en-wikipedia-org-3337	350	2	,	,	,
en-wikipedia-org-3337	350	3	Oskar	Oskar	NNP
en-wikipedia-org-3337	350	4	and	and	CC
en-wikipedia-org-3337	350	5	John	John	NNP
en-wikipedia-org-3337	350	6	von	von	NNP
en-wikipedia-org-3337	350	7	Neumann	Neumann	NNP
en-wikipedia-org-3337	350	8	(	(	-LRB-
en-wikipedia-org-3337	350	9	1947	1947	CD
en-wikipedia-org-3337	350	10	)	)	-RRB-
en-wikipedia-org-3337	350	11	The	the	DT
en-wikipedia-org-3337	350	12	Theory	Theory	NNP
en-wikipedia-org-3337	350	13	of	of	IN
en-wikipedia-org-3337	350	14	Games	Games	NNPS
en-wikipedia-org-3337	350	15	and	and	CC
en-wikipedia-org-3337	350	16	Economic	Economic	NNP
en-wikipedia-org-3337	350	17	Behavior	Behavior	NNP
en-wikipedia-org-3337	350	18	Princeton	Princeton	NNP
en-wikipedia-org-3337	350	19	University	University	NNP
en-wikipedia-org-3337	350	20	Press	Press	NNP
en-wikipedia-org-3337	350	21	Myerson	Myerson	NNP
en-wikipedia-org-3337	350	22	,	,	,
en-wikipedia-org-3337	350	23	Roger	Roger	NNP
en-wikipedia-org-3337	350	24	B.	B.	NNP
en-wikipedia-org-3337	351	1	(	(	-LRB-
en-wikipedia-org-3337	351	2	1997	1997	CD
en-wikipedia-org-3337	351	3	)	)	-RRB-
en-wikipedia-org-3337	351	4	,	,	,
en-wikipedia-org-3337	351	5	Game	game	NN
en-wikipedia-org-3337	351	6	theory	theory	NN
en-wikipedia-org-3337	351	7	:	:	:
en-wikipedia-org-3337	351	8	analysis	analysis	NN
en-wikipedia-org-3337	351	9	of	of	IN
en-wikipedia-org-3337	351	10	conflict	conflict	NN
en-wikipedia-org-3337	351	11	,	,	,
en-wikipedia-org-3337	351	12	Harvard	Harvard	NNP
en-wikipedia-org-3337	351	13	University	University	NNP
en-wikipedia-org-3337	351	14	Press	Press	NNP
en-wikipedia-org-3337	351	15	,	,	,
en-wikipedia-org-3337	351	16	ISBN	ISBN	NNP
en-wikipedia-org-3337	351	17	 	  	_SP
en-wikipedia-org-3337	351	18	978	978	CD
en-wikipedia-org-3337	351	19	-	-	HYPH
en-wikipedia-org-3337	351	20	0	0	CD
en-wikipedia-org-3337	351	21	-	-	HYPH
en-wikipedia-org-3337	351	22	674	674	CD
en-wikipedia-org-3337	351	23	-	-	HYPH
en-wikipedia-org-3337	351	24	34116	34116	CD
en-wikipedia-org-3337	351	25	-	-	HYPH
en-wikipedia-org-3337	351	26	6	6	CD
en-wikipedia-org-3337	351	27	Papayoanou	Papayoanou	NNP
en-wikipedia-org-3337	351	28	,	,	,
en-wikipedia-org-3337	351	29	Paul	Paul	NNP
en-wikipedia-org-3337	351	30	(	(	-LRB-
en-wikipedia-org-3337	351	31	2010	2010	CD
en-wikipedia-org-3337	351	32	)	)	-RRB-
en-wikipedia-org-3337	351	33	,	,	,
en-wikipedia-org-3337	351	34	Game	Game	NNP
en-wikipedia-org-3337	351	35	Theory	Theory	NNP
en-wikipedia-org-3337	351	36	for	for	IN
en-wikipedia-org-3337	351	37	Business	business	NN
en-wikipedia-org-3337	351	38	:	:	:
en-wikipedia-org-3337	351	39	A	A	NNP
en-wikipedia-org-3337	351	40	Primer	Primer	NNP
en-wikipedia-org-3337	351	41	in	in	IN
en-wikipedia-org-3337	351	42	Strategic	Strategic	NNP
en-wikipedia-org-3337	351	43	Gaming	Gaming	NNP
en-wikipedia-org-3337	351	44	,	,	,
en-wikipedia-org-3337	351	45	Probabilistic	Probabilistic	NNP
en-wikipedia-org-3337	351	46	Publishing	Publishing	NNP
en-wikipedia-org-3337	351	47	,	,	,
en-wikipedia-org-3337	351	48	ISBN	ISBN	NNP
en-wikipedia-org-3337	351	49	 	  	_SP
en-wikipedia-org-3337	351	50	978	978	CD
en-wikipedia-org-3337	351	51	-	-	HYPH
en-wikipedia-org-3337	351	52	0964793873	0964793873	CD
en-wikipedia-org-3337	351	53	Rubinstein	Rubinstein	NNP
en-wikipedia-org-3337	351	54	,	,	,
en-wikipedia-org-3337	351	55	Ariel	Ariel	NNP
en-wikipedia-org-3337	351	56	;	;	:
en-wikipedia-org-3337	351	57	Osborne	Osborne	NNP
en-wikipedia-org-3337	351	58	,	,	,
en-wikipedia-org-3337	351	59	Martin	Martin	NNP
en-wikipedia-org-3337	351	60	J.	J.	NNP
en-wikipedia-org-3337	352	1	(	(	-LRB-
en-wikipedia-org-3337	352	2	1994	1994	CD
en-wikipedia-org-3337	352	3	)	)	-RRB-
en-wikipedia-org-3337	352	4	,	,	,
en-wikipedia-org-3337	352	5	A	a	DT
en-wikipedia-org-3337	352	6	course	course	NN
en-wikipedia-org-3337	352	7	in	in	IN
en-wikipedia-org-3337	352	8	game	game	NN
en-wikipedia-org-3337	352	9	theory	theory	NN
en-wikipedia-org-3337	352	10	,	,	,
en-wikipedia-org-3337	352	11	MIT	MIT	NNP
en-wikipedia-org-3337	352	12	Press	Press	NNP
en-wikipedia-org-3337	352	13	,	,	,
en-wikipedia-org-3337	352	14	ISBN	ISBN	NNP
en-wikipedia-org-3337	352	15	 	  	_SP
en-wikipedia-org-3337	352	16	978	978	CD
en-wikipedia-org-3337	352	17	-	-	HYPH
en-wikipedia-org-3337	352	18	0	0	CD
en-wikipedia-org-3337	352	19	-	-	HYPH
en-wikipedia-org-3337	352	20	262	262	CD
en-wikipedia-org-3337	352	21	-	-	HYPH
en-wikipedia-org-3337	352	22	65040	65040	CD
en-wikipedia-org-3337	352	23	-	-	SYM
en-wikipedia-org-3337	352	24	3	3	CD
en-wikipedia-org-3337	352	25	.	.	.
en-wikipedia-org-3337	353	1	A	a	DT
en-wikipedia-org-3337	353	2	modern	modern	JJ
en-wikipedia-org-3337	353	3	introduction	introduction	NN
en-wikipedia-org-3337	353	4	at	at	IN
en-wikipedia-org-3337	353	5	the	the	DT
en-wikipedia-org-3337	353	6	graduate	graduate	NN
en-wikipedia-org-3337	353	7	level	level	NN
en-wikipedia-org-3337	353	8	.	.	.
en-wikipedia-org-3337	354	1	Shoham	Shoham	NNP
en-wikipedia-org-3337	354	2	,	,	,
en-wikipedia-org-3337	354	3	Yoav	yoav	NN
en-wikipedia-org-3337	354	4	;	;	:
en-wikipedia-org-3337	354	5	Leyton	Leyton	NNP
en-wikipedia-org-3337	354	6	-	-	HYPH
en-wikipedia-org-3337	354	7	Brown	Brown	NNP
en-wikipedia-org-3337	354	8	,	,	,
en-wikipedia-org-3337	354	9	Kevin	Kevin	NNP
en-wikipedia-org-3337	354	10	(	(	-LRB-
en-wikipedia-org-3337	354	11	2009	2009	CD
en-wikipedia-org-3337	354	12	)	)	-RRB-
en-wikipedia-org-3337	354	13	,	,	,
en-wikipedia-org-3337	354	14	Multiagent	Multiagent	NNP
en-wikipedia-org-3337	354	15	Systems	Systems	NNPS
en-wikipedia-org-3337	354	16	:	:	:
en-wikipedia-org-3337	354	17	Algorithmic	Algorithmic	NNP
en-wikipedia-org-3337	354	18	,	,	,
en-wikipedia-org-3337	354	19	Game	Game	NNP
en-wikipedia-org-3337	354	20	-	-	HYPH
en-wikipedia-org-3337	354	21	Theoretic	Theoretic	NNP
en-wikipedia-org-3337	354	22	,	,	,
en-wikipedia-org-3337	354	23	and	and	CC
en-wikipedia-org-3337	354	24	Logical	Logical	NNP
en-wikipedia-org-3337	354	25	Foundations	Foundations	NNPS
en-wikipedia-org-3337	354	26	,	,	,
en-wikipedia-org-3337	354	27	New	New	NNP
en-wikipedia-org-3337	354	28	York	York	NNP
en-wikipedia-org-3337	354	29	:	:	:
en-wikipedia-org-3337	354	30	Cambridge	Cambridge	NNP
en-wikipedia-org-3337	354	31	University	University	NNP
en-wikipedia-org-3337	354	32	Press	Press	NNP
en-wikipedia-org-3337	354	33	,	,	,
en-wikipedia-org-3337	354	34	ISBN	ISBN	NNP
en-wikipedia-org-3337	354	35	 	  	_SP
en-wikipedia-org-3337	354	36	978	978	CD
en-wikipedia-org-3337	354	37	-	-	HYPH
en-wikipedia-org-3337	354	38	0	0	CD
en-wikipedia-org-3337	354	39	-	-	HYPH
en-wikipedia-org-3337	354	40	521	521	CD
en-wikipedia-org-3337	354	41	-	-	HYPH
en-wikipedia-org-3337	354	42	89943	89943	CD
en-wikipedia-org-3337	354	43	-	-	SYM
en-wikipedia-org-3337	354	44	7	7	CD
en-wikipedia-org-3337	354	45	.	.	.
en-wikipedia-org-3337	355	1	A	a	DT
en-wikipedia-org-3337	355	2	comprehensive	comprehensive	JJ
en-wikipedia-org-3337	355	3	reference	reference	NN
en-wikipedia-org-3337	355	4	from	from	IN
en-wikipedia-org-3337	355	5	a	a	DT
en-wikipedia-org-3337	355	6	computational	computational	JJ
en-wikipedia-org-3337	355	7	perspective	perspective	NN
en-wikipedia-org-3337	355	8	;	;	:
en-wikipedia-org-3337	355	9	see	see	VB
en-wikipedia-org-3337	355	10	Chapter	chapter	NN
en-wikipedia-org-3337	355	11	3	3	CD
en-wikipedia-org-3337	355	12	.	.	.
en-wikipedia-org-3337	356	1	Downloadable	downloadable	JJ
en-wikipedia-org-3337	356	2	free	free	JJ
en-wikipedia-org-3337	356	3	online	online	RB
en-wikipedia-org-3337	356	4	.	.	.
en-wikipedia-org-3337	357	1	Gibbons	gibbon	NNS
en-wikipedia-org-3337	357	2	,	,	,
en-wikipedia-org-3337	357	3	Robert	Robert	NNP
en-wikipedia-org-3337	357	4	(	(	-LRB-
en-wikipedia-org-3337	357	5	1992	1992	CD
en-wikipedia-org-3337	357	6	)	)	-RRB-
en-wikipedia-org-3337	357	7	,	,	,
en-wikipedia-org-3337	357	8	Game	Game	NNP
en-wikipedia-org-3337	357	9	Theory	Theory	NNP
en-wikipedia-org-3337	357	10	for	for	IN
en-wikipedia-org-3337	357	11	Applied	Applied	NNP
en-wikipedia-org-3337	357	12	Economists	Economists	NNPS
en-wikipedia-org-3337	357	13	,	,	,
en-wikipedia-org-3337	357	14	Princeton	Princeton	NNP
en-wikipedia-org-3337	357	15	University	University	NNP
en-wikipedia-org-3337	357	16	Press	Press	NNP
en-wikipedia-org-3337	357	17	(	(	-LRB-
en-wikipedia-org-3337	357	18	July	July	NNP
en-wikipedia-org-3337	357	19	13	13	CD
en-wikipedia-org-3337	357	20	,	,	,
en-wikipedia-org-3337	357	21	1992	1992	CD
en-wikipedia-org-3337	357	22	)	)	-RRB-
en-wikipedia-org-3337	357	23	,	,	,
en-wikipedia-org-3337	357	24	ISBN	ISBN	NNP
en-wikipedia-org-3337	357	25	 	  	_SP
en-wikipedia-org-3337	357	26	978	978	CD
en-wikipedia-org-3337	357	27	-	-	HYPH
en-wikipedia-org-3337	357	28	0	0	CD
en-wikipedia-org-3337	357	29	-	-	HYPH
en-wikipedia-org-3337	357	30	691	691	CD
en-wikipedia-org-3337	357	31	-	-	HYPH
en-wikipedia-org-3337	357	32	00395	00395	CD
en-wikipedia-org-3337	357	33	-	-	HYPH
en-wikipedia-org-3337	357	34	5	5	CD
en-wikipedia-org-3337	357	35	.	.	.
en-wikipedia-org-3337	358	1	Lucid	lucid	JJ
en-wikipedia-org-3337	358	2	and	and	CC
en-wikipedia-org-3337	358	3	detailed	detailed	JJ
en-wikipedia-org-3337	358	4	introduction	introduction	NN
en-wikipedia-org-3337	358	5	to	to	IN
en-wikipedia-org-3337	358	6	game	game	NN
en-wikipedia-org-3337	358	7	theory	theory	NN
en-wikipedia-org-3337	358	8	in	in	IN
en-wikipedia-org-3337	358	9	an	an	DT
en-wikipedia-org-3337	358	10	explicitly	explicitly	RB
en-wikipedia-org-3337	358	11	economic	economic	JJ
en-wikipedia-org-3337	358	12	context	context	NN
en-wikipedia-org-3337	358	13	.	.	.
en-wikipedia-org-3337	359	1	Osborne	Osborne	NNP
en-wikipedia-org-3337	359	2	,	,	,
en-wikipedia-org-3337	359	3	Martin	Martin	NNP
en-wikipedia-org-3337	359	4	(	(	-LRB-
en-wikipedia-org-3337	359	5	2004	2004	CD
en-wikipedia-org-3337	359	6	)	)	-RRB-
en-wikipedia-org-3337	359	7	,	,	,
en-wikipedia-org-3337	359	8	An	an	DT
en-wikipedia-org-3337	359	9	introduction	introduction	NN
en-wikipedia-org-3337	359	10	to	to	IN
en-wikipedia-org-3337	359	11	game	game	NN
en-wikipedia-org-3337	359	12	theory	theory	NN
en-wikipedia-org-3337	359	13	,	,	,
en-wikipedia-org-3337	359	14	Oxford	Oxford	NNP
en-wikipedia-org-3337	359	15	University	University	NNP
en-wikipedia-org-3337	359	16	Press	Press	NNP
en-wikipedia-org-3337	359	17	,	,	,
en-wikipedia-org-3337	359	18	ISBN	ISBN	NNP
en-wikipedia-org-3337	359	19	 	  	_SP
en-wikipedia-org-3337	359	20	978	978	CD
en-wikipedia-org-3337	359	21	-	-	HYPH
en-wikipedia-org-3337	359	22	0	0	CD
en-wikipedia-org-3337	359	23	-	-	HYPH
en-wikipedia-org-3337	359	24	19	19	CD
en-wikipedia-org-3337	359	25	-	-	HYPH
en-wikipedia-org-3337	359	26	512895	512895	CD
en-wikipedia-org-3337	359	27	-	-	SYM
en-wikipedia-org-3337	359	28	6	6	CD
en-wikipedia-org-3337	359	29	.	.	.
en-wikipedia-org-3337	360	1	Introduction	introduction	NN
en-wikipedia-org-3337	360	2	to	to	IN
en-wikipedia-org-3337	360	3	Nash	Nash	NNP
en-wikipedia-org-3337	360	4	equilibrium	equilibrium	NN
en-wikipedia-org-3337	360	5	.	.	.
en-wikipedia-org-3337	361	1	Binmore	binmore	RB
en-wikipedia-org-3337	361	2	,	,	,
en-wikipedia-org-3337	361	3	Ken	Ken	NNP
en-wikipedia-org-3337	361	4	(	(	-LRB-
en-wikipedia-org-3337	361	5	2007	2007	CD
en-wikipedia-org-3337	361	6	)	)	-RRB-
en-wikipedia-org-3337	361	7	,	,	,
en-wikipedia-org-3337	361	8	Playing	play	VBG
en-wikipedia-org-3337	361	9	for	for	IN
en-wikipedia-org-3337	361	10	Real	real	JJ
en-wikipedia-org-3337	361	11	:	:	:
en-wikipedia-org-3337	361	12	A	a	DT
en-wikipedia-org-3337	361	13	Text	Text	NNP
en-wikipedia-org-3337	361	14	on	on	IN
en-wikipedia-org-3337	361	15	Game	Game	NNP
en-wikipedia-org-3337	361	16	Theory	Theory	NNP
en-wikipedia-org-3337	361	17	,	,	,
en-wikipedia-org-3337	361	18	Oxford	Oxford	NNP
en-wikipedia-org-3337	361	19	University	University	NNP
en-wikipedia-org-3337	361	20	Press	Press	NNP
en-wikipedia-org-3337	361	21	,	,	,
en-wikipedia-org-3337	361	22	ISBN	ISBN	NNP
en-wikipedia-org-3337	361	23	 	  	_SP
en-wikipedia-org-3337	361	24	978	978	CD
en-wikipedia-org-3337	361	25	-	-	HYPH
en-wikipedia-org-3337	361	26	0195300574	0195300574	CD
en-wikipedia-org-3337	361	27	.	.	.
en-wikipedia-org-3337	362	1	Original	original	JJ
en-wikipedia-org-3337	362	2	Nash	Nash	NNP
en-wikipedia-org-3337	362	3	papers[edit	papers[edit	NN
en-wikipedia-org-3337	362	4	]	]	-RRB-
en-wikipedia-org-3337	362	5	Nash	Nash	NNP
en-wikipedia-org-3337	362	6	,	,	,
en-wikipedia-org-3337	362	7	John	John	NNP
en-wikipedia-org-3337	362	8	(	(	-LRB-
en-wikipedia-org-3337	362	9	1950	1950	CD
en-wikipedia-org-3337	362	10	)	)	-RRB-
en-wikipedia-org-3337	362	11	"	"	``
en-wikipedia-org-3337	362	12	Equilibrium	equilibrium	NN
en-wikipedia-org-3337	362	13	points	point	NNS
en-wikipedia-org-3337	362	14	in	in	IN
en-wikipedia-org-3337	362	15	n	n	JJ
en-wikipedia-org-3337	362	16	-	-	HYPH
en-wikipedia-org-3337	362	17	person	person	NN
en-wikipedia-org-3337	362	18	games	game	NNS
en-wikipedia-org-3337	362	19	"	"	``
en-wikipedia-org-3337	362	20	Proceedings	Proceedings	NNPS
en-wikipedia-org-3337	362	21	of	of	IN
en-wikipedia-org-3337	362	22	the	the	DT
en-wikipedia-org-3337	362	23	National	National	NNP
en-wikipedia-org-3337	362	24	Academy	Academy	NNP
en-wikipedia-org-3337	362	25	of	of	IN
en-wikipedia-org-3337	362	26	Sciences	Sciences	NNPS
en-wikipedia-org-3337	362	27	36(1):48	36(1):48	NNP
en-wikipedia-org-3337	362	28	-	-	HYPH
en-wikipedia-org-3337	362	29	49	49	CD
en-wikipedia-org-3337	362	30	.	.	.
en-wikipedia-org-3337	363	1	Nash	Nash	NNP
en-wikipedia-org-3337	363	2	,	,	,
en-wikipedia-org-3337	363	3	John	John	NNP
en-wikipedia-org-3337	363	4	(	(	-LRB-
en-wikipedia-org-3337	363	5	1951	1951	CD
en-wikipedia-org-3337	363	6	)	)	-RRB-
en-wikipedia-org-3337	363	7	"	"	``
en-wikipedia-org-3337	363	8	Non	non	JJ
en-wikipedia-org-3337	363	9	-	-	JJ
en-wikipedia-org-3337	363	10	Cooperative	cooperative	JJ
en-wikipedia-org-3337	363	11	Games	Games	NNPS
en-wikipedia-org-3337	363	12	"	"	``
en-wikipedia-org-3337	363	13	The	The	NNP
en-wikipedia-org-3337	363	14	Annals	Annals	NNPS
en-wikipedia-org-3337	363	15	of	of	IN
en-wikipedia-org-3337	363	16	Mathematics	Mathematics	NNP
en-wikipedia-org-3337	363	17	54(2):286	54(2):286	CD
en-wikipedia-org-3337	363	18	-	-	HYPH
en-wikipedia-org-3337	363	19	295	295	CD
en-wikipedia-org-3337	363	20	.	.	.
en-wikipedia-org-3337	364	1	Other	other	JJ
en-wikipedia-org-3337	364	2	references[edit	references[edit	NNP
en-wikipedia-org-3337	364	3	]	]	-RRB-
en-wikipedia-org-3337	364	4	Mehlmann	Mehlmann	NNP
en-wikipedia-org-3337	364	5	,	,	,
en-wikipedia-org-3337	364	6	A.	a.	NN
en-wikipedia-org-3337	365	1	(	(	-LRB-
en-wikipedia-org-3337	365	2	2000	2000	CD
en-wikipedia-org-3337	365	3	)	)	-RRB-
en-wikipedia-org-3337	365	4	The	the	DT
en-wikipedia-org-3337	365	5	Game	Game	NNP
en-wikipedia-org-3337	365	6	's	's	POS
en-wikipedia-org-3337	365	7	Afoot	Afoot	NNP
en-wikipedia-org-3337	365	8	!	!	.
en-wikipedia-org-3337	366	1	Game	Game	NNP
en-wikipedia-org-3337	366	2	Theory	Theory	NNP
en-wikipedia-org-3337	366	3	in	in	IN
en-wikipedia-org-3337	366	4	Myth	Myth	NNP
en-wikipedia-org-3337	366	5	and	and	CC
en-wikipedia-org-3337	366	6	Paradox	Paradox	NNP
en-wikipedia-org-3337	366	7	,	,	,
en-wikipedia-org-3337	366	8	American	American	NNP
en-wikipedia-org-3337	366	9	Mathematical	Mathematical	NNP
en-wikipedia-org-3337	366	10	Society	Society	NNP
en-wikipedia-org-3337	366	11	.	.	.
en-wikipedia-org-3337	367	1	Nasar	Nasar	NNP
en-wikipedia-org-3337	367	2	,	,	,
en-wikipedia-org-3337	367	3	Sylvia	Sylvia	NNP
en-wikipedia-org-3337	367	4	(	(	-LRB-
en-wikipedia-org-3337	367	5	1998	1998	CD
en-wikipedia-org-3337	367	6	)	)	-RRB-
en-wikipedia-org-3337	367	7	,	,	,
en-wikipedia-org-3337	367	8	A	a	DT
en-wikipedia-org-3337	367	9	Beautiful	beautiful	JJ
en-wikipedia-org-3337	367	10	Mind	mind	NN
en-wikipedia-org-3337	367	11	,	,	,
en-wikipedia-org-3337	367	12	Simon	Simon	NNP
en-wikipedia-org-3337	367	13	&	&	CC
en-wikipedia-org-3337	367	14	Schuster	Schuster	NNP
en-wikipedia-org-3337	367	15	.	.	.
en-wikipedia-org-3337	368	1	External	external	JJ
en-wikipedia-org-3337	368	2	links[edit	links[edit	,
en-wikipedia-org-3337	368	3	]	]	-RRB-
en-wikipedia-org-3337	368	4	"	"	``
en-wikipedia-org-3337	368	5	Nash	Nash	NNP
en-wikipedia-org-3337	368	6	theorem	theorem	NN
en-wikipedia-org-3337	368	7	(	(	-LRB-
en-wikipedia-org-3337	368	8	in	in	IN
en-wikipedia-org-3337	368	9	game	game	NN
en-wikipedia-org-3337	368	10	theory	theory	NN
en-wikipedia-org-3337	368	11	)	)	-RRB-
en-wikipedia-org-3337	368	12	"	"	''
en-wikipedia-org-3337	368	13	,	,	,
en-wikipedia-org-3337	368	14	Encyclopedia	Encyclopedia	NNP
en-wikipedia-org-3337	368	15	of	of	IN
en-wikipedia-org-3337	368	16	Mathematics	Mathematics	NNP
en-wikipedia-org-3337	368	17	,	,	,
en-wikipedia-org-3337	368	18	EMS	EMS	NNP
en-wikipedia-org-3337	368	19	Press	Press	NNP
en-wikipedia-org-3337	368	20	,	,	,
en-wikipedia-org-3337	368	21	2001	2001	CD
en-wikipedia-org-3337	368	22	[	[	-LRB-
en-wikipedia-org-3337	368	23	1994	1994	CD
en-wikipedia-org-3337	368	24	]	]	-RRB-
en-wikipedia-org-3337	368	25	Complete	Complete	NNP
en-wikipedia-org-3337	368	26	Proof	Proof	NNP
en-wikipedia-org-3337	368	27	of	of	IN
en-wikipedia-org-3337	368	28	Existence	Existence	NNP
en-wikipedia-org-3337	368	29	of	of	IN
en-wikipedia-org-3337	368	30	Nash	Nash	NNP
en-wikipedia-org-3337	368	31	Equilibria	Equilibria	NNP
en-wikipedia-org-3337	368	32	Simplified	Simplified	NNP
en-wikipedia-org-3337	368	33	Form	Form	NNP
en-wikipedia-org-3337	368	34	and	and	CC
en-wikipedia-org-3337	368	35	Related	Related	NNP
en-wikipedia-org-3337	368	36	Results	Results	NNPS
en-wikipedia-org-3337	368	37	v	v	NN
en-wikipedia-org-3337	368	38	t	t	NN
en-wikipedia-org-3337	368	39	e	e	NN
en-wikipedia-org-3337	368	40	Topics	Topics	NNP
en-wikipedia-org-3337	368	41	in	in	IN
en-wikipedia-org-3337	368	42	game	game	NN
en-wikipedia-org-3337	368	43	theory	theory	NN
en-wikipedia-org-3337	368	44	Definitions	definition	NNS
en-wikipedia-org-3337	368	45	Cooperative	cooperative	JJ
en-wikipedia-org-3337	368	46	game	game	NN
en-wikipedia-org-3337	368	47	Determinacy	Determinacy	NNP
en-wikipedia-org-3337	368	48	Escalation	Escalation	NNP
en-wikipedia-org-3337	368	49	of	of	IN
en-wikipedia-org-3337	368	50	commitment	commitment	JJ
en-wikipedia-org-3337	368	51	Extensive	extensive	JJ
en-wikipedia-org-3337	368	52	-	-	HYPH
en-wikipedia-org-3337	368	53	form	form	NN
en-wikipedia-org-3337	368	54	game	game	NN
en-wikipedia-org-3337	368	55	First	first	JJ
en-wikipedia-org-3337	368	56	-	-	HYPH
en-wikipedia-org-3337	368	57	player	player	NN
en-wikipedia-org-3337	368	58	and	and	CC
en-wikipedia-org-3337	368	59	second	second	JJ
en-wikipedia-org-3337	368	60	-	-	HYPH
en-wikipedia-org-3337	368	61	player	player	NN
en-wikipedia-org-3337	368	62	win	win	NN
en-wikipedia-org-3337	368	63	Game	Game	NNP
en-wikipedia-org-3337	368	64	complexity	complexity	NN
en-wikipedia-org-3337	368	65	Graphical	graphical	JJ
en-wikipedia-org-3337	368	66	game	game	NN
en-wikipedia-org-3337	368	67	Hierarchy	Hierarchy	NNP
en-wikipedia-org-3337	368	68	of	of	IN
en-wikipedia-org-3337	368	69	beliefs	belief	NNS
en-wikipedia-org-3337	368	70	Information	information	NN
en-wikipedia-org-3337	368	71	set	set	VBD
en-wikipedia-org-3337	368	72	Normal	normal	JJ
en-wikipedia-org-3337	368	73	-	-	HYPH
en-wikipedia-org-3337	368	74	form	form	NN
en-wikipedia-org-3337	368	75	game	game	NN
en-wikipedia-org-3337	368	76	Preference	Preference	NNP
en-wikipedia-org-3337	368	77	Sequential	Sequential	NNP
en-wikipedia-org-3337	368	78	game	game	NN
en-wikipedia-org-3337	368	79	Simultaneous	simultaneous	JJ
en-wikipedia-org-3337	368	80	game	game	NN
en-wikipedia-org-3337	368	81	Simultaneous	simultaneous	JJ
en-wikipedia-org-3337	368	82	action	action	NN
en-wikipedia-org-3337	368	83	selection	selection	NN
en-wikipedia-org-3337	368	84	Solved	solved	JJ
en-wikipedia-org-3337	368	85	game	game	NN
en-wikipedia-org-3337	368	86	Succinct	succinct	JJ
en-wikipedia-org-3337	368	87	game	game	NN
en-wikipedia-org-3337	368	88	Equilibrium	Equilibrium	NNP
en-wikipedia-org-3337	368	89	concepts	concept	VBZ
en-wikipedia-org-3337	368	90	Nash	Nash	NNP
en-wikipedia-org-3337	368	91	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	92	Subgame	subgame	NN
en-wikipedia-org-3337	368	93	perfection	perfection	NN
en-wikipedia-org-3337	368	94	Mertens	Mertens	NNP
en-wikipedia-org-3337	368	95	-	-	HYPH
en-wikipedia-org-3337	368	96	stable	stable	JJ
en-wikipedia-org-3337	368	97	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	98	Bayesian	Bayesian	NNP
en-wikipedia-org-3337	368	99	Nash	Nash	NNP
en-wikipedia-org-3337	368	100	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	101	Perfect	perfect	JJ
en-wikipedia-org-3337	368	102	Bayesian	bayesian	JJ
en-wikipedia-org-3337	368	103	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	104	Trembling	tremble	VBG
en-wikipedia-org-3337	368	105	hand	hand	NN
en-wikipedia-org-3337	368	106	Proper	proper	JJ
en-wikipedia-org-3337	368	107	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	108	Epsilon	epsilon	NN
en-wikipedia-org-3337	368	109	-	-	HYPH
en-wikipedia-org-3337	368	110	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	111	Correlated	correlate	VBN
en-wikipedia-org-3337	368	112	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	113	Sequential	sequential	JJ
en-wikipedia-org-3337	368	114	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	115	Quasi	Quasi	NNP
en-wikipedia-org-3337	368	116	-	-	HYPH
en-wikipedia-org-3337	368	117	perfect	perfect	JJ
en-wikipedia-org-3337	368	118	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	119	Evolutionarily	evolutionarily	RB
en-wikipedia-org-3337	368	120	stable	stable	JJ
en-wikipedia-org-3337	368	121	strategy	strategy	NN
en-wikipedia-org-3337	368	122	Risk	risk	NN
en-wikipedia-org-3337	368	123	dominance	dominance	NN
en-wikipedia-org-3337	368	124	Core	Core	NNP
en-wikipedia-org-3337	368	125	Shapley	Shapley	NNP
en-wikipedia-org-3337	368	126	value	value	NN
en-wikipedia-org-3337	368	127	Pareto	Pareto	NNP
en-wikipedia-org-3337	368	128	efficiency	efficiency	NN
en-wikipedia-org-3337	368	129	Gibbs	Gibbs	NNPS
en-wikipedia-org-3337	368	130	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	131	Quantal	quantal	JJ
en-wikipedia-org-3337	368	132	response	response	NN
en-wikipedia-org-3337	368	133	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	134	Self	self	NN
en-wikipedia-org-3337	368	135	-	-	HYPH
en-wikipedia-org-3337	368	136	confirming	confirm	VBG
en-wikipedia-org-3337	368	137	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	138	Strong	Strong	NNP
en-wikipedia-org-3337	368	139	Nash	Nash	NNP
en-wikipedia-org-3337	368	140	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	141	Markov	Markov	NNP
en-wikipedia-org-3337	368	142	perfect	perfect	JJ
en-wikipedia-org-3337	368	143	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	144	Strategies	strategy	NNS
en-wikipedia-org-3337	368	145	Dominant	dominant	JJ
en-wikipedia-org-3337	368	146	strategies	strategy	NNS
en-wikipedia-org-3337	368	147	Pure	pure	JJ
en-wikipedia-org-3337	368	148	strategy	strategy	NN
en-wikipedia-org-3337	368	149	Mixed	mixed	JJ
en-wikipedia-org-3337	368	150	strategy	strategy	NN
en-wikipedia-org-3337	368	151	Strategy	strategy	NN
en-wikipedia-org-3337	368	152	-	-	HYPH
en-wikipedia-org-3337	368	153	stealing	steal	VBG
en-wikipedia-org-3337	368	154	argument	argument	NN
en-wikipedia-org-3337	368	155	Tit	Tit	NNP
en-wikipedia-org-3337	368	156	for	for	IN
en-wikipedia-org-3337	368	157	tat	tat	NNP
en-wikipedia-org-3337	368	158	Grim	Grim	NNP
en-wikipedia-org-3337	368	159	trigger	trigger	NN
en-wikipedia-org-3337	368	160	Collusion	Collusion	NNP
en-wikipedia-org-3337	368	161	Backward	Backward	NNP
en-wikipedia-org-3337	368	162	induction	induction	NN
en-wikipedia-org-3337	368	163	Forward	Forward	NNP
en-wikipedia-org-3337	368	164	induction	induction	NN
en-wikipedia-org-3337	368	165	Markov	Markov	NNP
en-wikipedia-org-3337	368	166	strategy	strategy	NN
en-wikipedia-org-3337	368	167	Bid	Bid	NNP
en-wikipedia-org-3337	368	168	shading	shade	VBG
en-wikipedia-org-3337	368	169	Classes	class	NNS
en-wikipedia-org-3337	368	170	of	of	IN
en-wikipedia-org-3337	368	171	games	game	NNS
en-wikipedia-org-3337	368	172	Symmetric	symmetric	JJ
en-wikipedia-org-3337	368	173	game	game	NN
en-wikipedia-org-3337	368	174	Perfect	perfect	JJ
en-wikipedia-org-3337	368	175	information	information	NN
en-wikipedia-org-3337	368	176	Repeated	repeat	VBN
en-wikipedia-org-3337	368	177	game	game	NN
en-wikipedia-org-3337	368	178	Signaling	signal	VBG
en-wikipedia-org-3337	368	179	game	game	NN
en-wikipedia-org-3337	368	180	Screening	screening	NN
en-wikipedia-org-3337	368	181	game	game	NN
en-wikipedia-org-3337	368	182	Cheap	cheap	JJ
en-wikipedia-org-3337	368	183	talk	talk	NN
en-wikipedia-org-3337	368	184	Zero	zero	CD
en-wikipedia-org-3337	368	185	-	-	HYPH
en-wikipedia-org-3337	368	186	sum	sum	NN
en-wikipedia-org-3337	368	187	game	game	NN
en-wikipedia-org-3337	368	188	Mechanism	Mechanism	NNP
en-wikipedia-org-3337	368	189	design	design	NN
en-wikipedia-org-3337	368	190	Bargaining	bargaining	NN
en-wikipedia-org-3337	368	191	problem	problem	NN
en-wikipedia-org-3337	368	192	Stochastic	stochastic	JJ
en-wikipedia-org-3337	368	193	game	game	NN
en-wikipedia-org-3337	368	194	Mean	mean	JJ
en-wikipedia-org-3337	368	195	field	field	NN
en-wikipedia-org-3337	368	196	game	game	NN
en-wikipedia-org-3337	368	197	n	n	NN
en-wikipedia-org-3337	368	198	-	-	HYPH
en-wikipedia-org-3337	368	199	player	player	NN
en-wikipedia-org-3337	368	200	game	game	NN
en-wikipedia-org-3337	368	201	Large	large	JJ
en-wikipedia-org-3337	368	202	Poisson	Poisson	NNP
en-wikipedia-org-3337	368	203	game	game	NN
en-wikipedia-org-3337	368	204	Nontransitive	Nontransitive	NNP
en-wikipedia-org-3337	368	205	game	game	NN
en-wikipedia-org-3337	368	206	Global	global	JJ
en-wikipedia-org-3337	368	207	game	game	NN
en-wikipedia-org-3337	368	208	Strictly	strictly	RB
en-wikipedia-org-3337	368	209	determined	determine	VBN
en-wikipedia-org-3337	368	210	game	game	NN
en-wikipedia-org-3337	368	211	Potential	potential	JJ
en-wikipedia-org-3337	368	212	game	game	NN
en-wikipedia-org-3337	368	213	Games	Games	NNPS
en-wikipedia-org-3337	368	214	Go	Go	NNP
en-wikipedia-org-3337	368	215	Chess	Chess	NNP
en-wikipedia-org-3337	368	216	Infinite	Infinite	NNP
en-wikipedia-org-3337	368	217	chess	chess	NN
en-wikipedia-org-3337	368	218	Checkers	Checkers	NNP
en-wikipedia-org-3337	368	219	Tic	Tic	NNP
en-wikipedia-org-3337	368	220	-	-	HYPH
en-wikipedia-org-3337	368	221	tac	tac	NN
en-wikipedia-org-3337	368	222	-	-	HYPH
en-wikipedia-org-3337	368	223	toe	toe	NNP
en-wikipedia-org-3337	368	224	Prisoner	Prisoner	NNP
en-wikipedia-org-3337	368	225	's	's	POS
en-wikipedia-org-3337	368	226	dilemma	dilemma	NN
en-wikipedia-org-3337	368	227	Gift	Gift	NNP
en-wikipedia-org-3337	368	228	-	-	HYPH
en-wikipedia-org-3337	368	229	exchange	exchange	NN
en-wikipedia-org-3337	368	230	game	game	NN
en-wikipedia-org-3337	368	231	Optional	optional	JJ
en-wikipedia-org-3337	368	232	prisoner	prisoner	NN
en-wikipedia-org-3337	368	233	's	's	POS
en-wikipedia-org-3337	368	234	dilemma	dilemma	NN
en-wikipedia-org-3337	368	235	Traveler	Traveler	NNP
en-wikipedia-org-3337	368	236	's	's	POS
en-wikipedia-org-3337	368	237	dilemma	dilemma	NN
en-wikipedia-org-3337	368	238	Coordination	Coordination	NNP
en-wikipedia-org-3337	368	239	game	game	NN
en-wikipedia-org-3337	368	240	Chicken	Chicken	NNP
en-wikipedia-org-3337	368	241	Centipede	Centipede	NNP
en-wikipedia-org-3337	368	242	game	game	NN
en-wikipedia-org-3337	368	243	Volunteer	Volunteer	NNP
en-wikipedia-org-3337	368	244	's	's	POS
en-wikipedia-org-3337	368	245	dilemma	dilemma	NN
en-wikipedia-org-3337	368	246	Dollar	Dollar	NNP
en-wikipedia-org-3337	368	247	auction	auction	NN
en-wikipedia-org-3337	368	248	Battle	Battle	NNP
en-wikipedia-org-3337	368	249	of	of	IN
en-wikipedia-org-3337	368	250	the	the	DT
en-wikipedia-org-3337	368	251	sexes	sex	NNS
en-wikipedia-org-3337	368	252	Stag	stag	JJ
en-wikipedia-org-3337	368	253	hunt	hunt	NN
en-wikipedia-org-3337	368	254	Matching	Matching	NNP
en-wikipedia-org-3337	368	255	pennies	penny	NNS
en-wikipedia-org-3337	368	256	Ultimatum	Ultimatum	NNP
en-wikipedia-org-3337	368	257	game	game	NN
en-wikipedia-org-3337	368	258	Rock	Rock	NNP
en-wikipedia-org-3337	368	259	paper	paper	NN
en-wikipedia-org-3337	368	260	scissors	scissor	NNS
en-wikipedia-org-3337	368	261	Pirate	Pirate	NNP
en-wikipedia-org-3337	368	262	game	game	NN
en-wikipedia-org-3337	368	263	Dictator	Dictator	NNP
en-wikipedia-org-3337	368	264	game	game	NN
en-wikipedia-org-3337	368	265	Public	public	JJ
en-wikipedia-org-3337	368	266	goods	good	NNS
en-wikipedia-org-3337	368	267	game	game	NN
en-wikipedia-org-3337	368	268	Blotto	Blotto	NNP
en-wikipedia-org-3337	368	269	game	game	NN
en-wikipedia-org-3337	368	270	War	War	NNP
en-wikipedia-org-3337	368	271	of	of	IN
en-wikipedia-org-3337	368	272	attrition	attrition	NN
en-wikipedia-org-3337	368	273	El	El	NNP
en-wikipedia-org-3337	368	274	Farol	Farol	NNP
en-wikipedia-org-3337	368	275	Bar	Bar	NNP
en-wikipedia-org-3337	368	276	problem	problem	NN
en-wikipedia-org-3337	368	277	Fair	Fair	NNP
en-wikipedia-org-3337	368	278	division	division	NN
en-wikipedia-org-3337	368	279	Fair	fair	JJ
en-wikipedia-org-3337	368	280	cake	cake	NN
en-wikipedia-org-3337	368	281	-	-	HYPH
en-wikipedia-org-3337	368	282	cutting	cut	VBG
en-wikipedia-org-3337	368	283	Cournot	Cournot	NNP
en-wikipedia-org-3337	368	284	game	game	NN
en-wikipedia-org-3337	368	285	Deadlock	Deadlock	NNP
en-wikipedia-org-3337	368	286	Diner	Diner	NNP
en-wikipedia-org-3337	368	287	's	's	POS
en-wikipedia-org-3337	368	288	dilemma	dilemma	NN
en-wikipedia-org-3337	368	289	Guess	Guess	NNP
en-wikipedia-org-3337	368	290	2/3	2/3	CD
en-wikipedia-org-3337	368	291	of	of	IN
en-wikipedia-org-3337	368	292	the	the	DT
en-wikipedia-org-3337	368	293	average	average	JJ
en-wikipedia-org-3337	368	294	Kuhn	Kuhn	NNP
en-wikipedia-org-3337	368	295	poker	poker	NN
en-wikipedia-org-3337	368	296	Nash	Nash	NNP
en-wikipedia-org-3337	368	297	bargaining	bargaining	NN
en-wikipedia-org-3337	368	298	game	game	NN
en-wikipedia-org-3337	368	299	Induction	Induction	NNP
en-wikipedia-org-3337	368	300	puzzles	puzzle	NNS
en-wikipedia-org-3337	368	301	Trust	Trust	NNP
en-wikipedia-org-3337	368	302	game	game	NN
en-wikipedia-org-3337	368	303	Princess	Princess	NNP
en-wikipedia-org-3337	368	304	and	and	CC
en-wikipedia-org-3337	368	305	Monster	Monster	NNP
en-wikipedia-org-3337	368	306	game	game	NN
en-wikipedia-org-3337	368	307	Rendezvous	rendezvous	JJ
en-wikipedia-org-3337	368	308	problem	problem	NN
en-wikipedia-org-3337	368	309	Theorems	Theorems	NNPS
en-wikipedia-org-3337	368	310	Arrow	Arrow	NNP
en-wikipedia-org-3337	368	311	's	's	POS
en-wikipedia-org-3337	368	312	impossibility	impossibility	NN
en-wikipedia-org-3337	368	313	theorem	theorem	NN
en-wikipedia-org-3337	368	314	Aumann	Aumann	NNP
en-wikipedia-org-3337	368	315	's	's	POS
en-wikipedia-org-3337	368	316	agreement	agreement	NN
en-wikipedia-org-3337	368	317	theorem	theorem	NN
en-wikipedia-org-3337	368	318	Folk	Folk	NNP
en-wikipedia-org-3337	368	319	theorem	theorem	NN
en-wikipedia-org-3337	368	320	Minimax	Minimax	NNP
en-wikipedia-org-3337	368	321	theorem	theorem	NN
en-wikipedia-org-3337	368	322	Nash	Nash	NNP
en-wikipedia-org-3337	368	323	's	's	POS
en-wikipedia-org-3337	368	324	theorem	theorem	JJ
en-wikipedia-org-3337	368	325	Purification	Purification	NNP
en-wikipedia-org-3337	368	326	theorem	theorem	JJ
en-wikipedia-org-3337	368	327	Revelation	Revelation	NNP
en-wikipedia-org-3337	368	328	principle	principle	NN
en-wikipedia-org-3337	368	329	Zermelo	Zermelo	NNP
en-wikipedia-org-3337	368	330	's	's	POS
en-wikipedia-org-3337	368	331	theorem	theorem	JJ
en-wikipedia-org-3337	368	332	Key	key	JJ
en-wikipedia-org-3337	368	333	figures	figure	NNS
en-wikipedia-org-3337	368	334	Albert	Albert	NNP
en-wikipedia-org-3337	368	335	W.	W.	NNP
en-wikipedia-org-3337	368	336	Tucker	Tucker	NNP
en-wikipedia-org-3337	368	337	Amos	Amos	NNP
en-wikipedia-org-3337	368	338	Tversky	Tversky	NNP
en-wikipedia-org-3337	368	339	Antoine	Antoine	NNP
en-wikipedia-org-3337	368	340	Augustin	Augustin	NNP
en-wikipedia-org-3337	368	341	Cournot	Cournot	NNP
en-wikipedia-org-3337	368	342	Ariel	Ariel	NNP
en-wikipedia-org-3337	368	343	Rubinstein	Rubinstein	NNP
en-wikipedia-org-3337	368	344	Claude	Claude	NNP
en-wikipedia-org-3337	368	345	Shannon	Shannon	NNP
en-wikipedia-org-3337	368	346	Daniel	Daniel	NNP
en-wikipedia-org-3337	368	347	Kahneman	Kahneman	NNP
en-wikipedia-org-3337	368	348	David	David	NNP
en-wikipedia-org-3337	368	349	K.	K.	NNP
en-wikipedia-org-3337	368	350	Levine	Levine	NNP
en-wikipedia-org-3337	368	351	David	David	NNP
en-wikipedia-org-3337	368	352	M.	M.	NNP
en-wikipedia-org-3337	368	353	Kreps	Kreps	NNP
en-wikipedia-org-3337	368	354	Donald	Donald	NNP
en-wikipedia-org-3337	368	355	B.	B.	NNP
en-wikipedia-org-3337	368	356	Gillies	Gillies	NNP
en-wikipedia-org-3337	368	357	Drew	Drew	NNP
en-wikipedia-org-3337	368	358	Fudenberg	Fudenberg	NNP
en-wikipedia-org-3337	368	359	Eric	Eric	NNP
en-wikipedia-org-3337	368	360	Maskin	Maskin	NNP
en-wikipedia-org-3337	368	361	Harold	Harold	NNP
en-wikipedia-org-3337	368	362	W.	W.	NNP
en-wikipedia-org-3337	368	363	Kuhn	Kuhn	NNP
en-wikipedia-org-3337	368	364	Herbert	Herbert	NNP
en-wikipedia-org-3337	368	365	Simon	Simon	NNP
en-wikipedia-org-3337	368	366	Hervé	Hervé	NNP
en-wikipedia-org-3337	368	367	Moulin	Moulin	NNP
en-wikipedia-org-3337	368	368	Jean	Jean	NNP
en-wikipedia-org-3337	368	369	Tirole	Tirole	NNP
en-wikipedia-org-3337	368	370	Jean	Jean	NNP
en-wikipedia-org-3337	368	371	-	-	HYPH
en-wikipedia-org-3337	368	372	François	François	NNP
en-wikipedia-org-3337	368	373	Mertens	Mertens	NNPS
en-wikipedia-org-3337	368	374	Jennifer	Jennifer	NNP
en-wikipedia-org-3337	368	375	Tour	Tour	NNP
en-wikipedia-org-3337	368	376	Chayes	Chayes	NNP
en-wikipedia-org-3337	368	377	John	John	NNP
en-wikipedia-org-3337	368	378	Harsanyi	Harsanyi	NNP
en-wikipedia-org-3337	368	379	John	John	NNP
en-wikipedia-org-3337	368	380	Maynard	Maynard	NNP
en-wikipedia-org-3337	368	381	Smith	Smith	NNP
en-wikipedia-org-3337	368	382	John	John	NNP
en-wikipedia-org-3337	368	383	Nash	Nash	NNP
en-wikipedia-org-3337	368	384	John	John	NNP
en-wikipedia-org-3337	368	385	von	von	NNP
en-wikipedia-org-3337	368	386	Neumann	Neumann	NNP
en-wikipedia-org-3337	368	387	Kenneth	Kenneth	NNP
en-wikipedia-org-3337	368	388	Arrow	Arrow	NNP
en-wikipedia-org-3337	368	389	Kenneth	Kenneth	NNP
en-wikipedia-org-3337	368	390	Binmore	Binmore	NNP
en-wikipedia-org-3337	368	391	Leonid	Leonid	NNP
en-wikipedia-org-3337	368	392	Hurwicz	Hurwicz	NNP
en-wikipedia-org-3337	368	393	Lloyd	Lloyd	NNP
en-wikipedia-org-3337	368	394	Shapley	Shapley	NNP
en-wikipedia-org-3337	368	395	Melvin	Melvin	NNP
en-wikipedia-org-3337	368	396	Dresher	Dresher	NNP
en-wikipedia-org-3337	368	397	Merrill	Merrill	NNP
en-wikipedia-org-3337	368	398	M.	M.	NNP
en-wikipedia-org-3337	368	399	Flood	Flood	NNP
en-wikipedia-org-3337	368	400	Olga	Olga	NNP
en-wikipedia-org-3337	368	401	Bondareva	Bondareva	NNP
en-wikipedia-org-3337	368	402	Oskar	Oskar	NNP
en-wikipedia-org-3337	368	403	Morgenstern	Morgenstern	NNP
en-wikipedia-org-3337	368	404	Paul	Paul	NNP
en-wikipedia-org-3337	368	405	Milgrom	Milgrom	NNP
en-wikipedia-org-3337	368	406	Peyton	Peyton	NNP
en-wikipedia-org-3337	368	407	Young	Young	NNP
en-wikipedia-org-3337	368	408	Reinhard	Reinhard	NNP
en-wikipedia-org-3337	368	409	Selten	Selten	NNP
en-wikipedia-org-3337	368	410	Robert	Robert	NNP
en-wikipedia-org-3337	368	411	Axelrod	Axelrod	NNP
en-wikipedia-org-3337	368	412	Robert	Robert	NNP
en-wikipedia-org-3337	368	413	Aumann	Aumann	NNP
en-wikipedia-org-3337	368	414	Robert	Robert	NNP
en-wikipedia-org-3337	368	415	B.	B.	NNP
en-wikipedia-org-3337	368	416	Wilson	Wilson	NNP
en-wikipedia-org-3337	368	417	Roger	Roger	NNP
en-wikipedia-org-3337	368	418	Myerson	Myerson	NNP
en-wikipedia-org-3337	368	419	Samuel	Samuel	NNP
en-wikipedia-org-3337	368	420	Bowles	Bowles	NNP
en-wikipedia-org-3337	368	421	Suzanne	Suzanne	NNP
en-wikipedia-org-3337	368	422	Scotchmer	Scotchmer	NNP
en-wikipedia-org-3337	368	423	Thomas	Thomas	NNP
en-wikipedia-org-3337	368	424	Schelling	Schelling	NNP
en-wikipedia-org-3337	368	425	William	William	NNP
en-wikipedia-org-3337	368	426	Vickrey	Vickrey	NNP
en-wikipedia-org-3337	368	427	See	see	VB
en-wikipedia-org-3337	368	428	also	also	RB
en-wikipedia-org-3337	368	429	All	all	DT
en-wikipedia-org-3337	368	430	-	-	HYPH
en-wikipedia-org-3337	368	431	pay	pay	VB
en-wikipedia-org-3337	368	432	auction	auction	NN
en-wikipedia-org-3337	368	433	Alpha	alpha	NN
en-wikipedia-org-3337	368	434	–	–	:
en-wikipedia-org-3337	368	435	beta	beta	NN
en-wikipedia-org-3337	368	436	pruning	prune	VBG
en-wikipedia-org-3337	368	437	Bertrand	Bertrand	NNP
en-wikipedia-org-3337	368	438	paradox	paradox	NN
en-wikipedia-org-3337	368	439	Bounded	bound	VBN
en-wikipedia-org-3337	368	440	rationality	rationality	NN
en-wikipedia-org-3337	368	441	Combinatorial	combinatorial	JJ
en-wikipedia-org-3337	368	442	game	game	NN
en-wikipedia-org-3337	368	443	theory	theory	NN
en-wikipedia-org-3337	368	444	Confrontation	Confrontation	NNP
en-wikipedia-org-3337	368	445	analysis	analysis	NN
en-wikipedia-org-3337	368	446	Coopetition	Coopetition	NNP
en-wikipedia-org-3337	368	447	Evolutionary	Evolutionary	NNP
en-wikipedia-org-3337	368	448	game	game	NN
en-wikipedia-org-3337	368	449	theory	theory	NN
en-wikipedia-org-3337	368	450	First	first	JJ
en-wikipedia-org-3337	368	451	-	-	HYPH
en-wikipedia-org-3337	368	452	move	move	NN
en-wikipedia-org-3337	368	453	advantage	advantage	NN
en-wikipedia-org-3337	368	454	in	in	IN
en-wikipedia-org-3337	368	455	chess	chess	NN
en-wikipedia-org-3337	368	456	Game	Game	NNP
en-wikipedia-org-3337	368	457	mechanics	mechanic	NNS
en-wikipedia-org-3337	368	458	Glossary	Glossary	NNP
en-wikipedia-org-3337	368	459	of	of	IN
en-wikipedia-org-3337	368	460	game	game	NN
en-wikipedia-org-3337	368	461	theory	theory	NN
en-wikipedia-org-3337	368	462	List	List	NNP
en-wikipedia-org-3337	368	463	of	of	IN
en-wikipedia-org-3337	368	464	game	game	NN
en-wikipedia-org-3337	368	465	theorists	theorist	NNS
en-wikipedia-org-3337	368	466	List	List	NNP
en-wikipedia-org-3337	368	467	of	of	IN
en-wikipedia-org-3337	368	468	games	game	NNS
en-wikipedia-org-3337	368	469	in	in	IN
en-wikipedia-org-3337	368	470	game	game	NN
en-wikipedia-org-3337	368	471	theory	theory	NN
en-wikipedia-org-3337	368	472	No	no	DT
en-wikipedia-org-3337	368	473	-	-	HYPH
en-wikipedia-org-3337	368	474	win	win	NN
en-wikipedia-org-3337	368	475	situation	situation	NN
en-wikipedia-org-3337	368	476	Solving	solve	VBG
en-wikipedia-org-3337	368	477	chess	chess	NN
en-wikipedia-org-3337	368	478	Topological	topological	JJ
en-wikipedia-org-3337	368	479	game	game	NN
en-wikipedia-org-3337	368	480	Tragedy	Tragedy	NNP
en-wikipedia-org-3337	368	481	of	of	IN
en-wikipedia-org-3337	368	482	the	the	DT
en-wikipedia-org-3337	368	483	commons	common	NNS
en-wikipedia-org-3337	368	484	Tyranny	tyranny	NN
en-wikipedia-org-3337	368	485	of	of	IN
en-wikipedia-org-3337	368	486	small	small	JJ
en-wikipedia-org-3337	368	487	decisions	decision	NNS
en-wikipedia-org-3337	368	488	Retrieved	retrieve	VBN
en-wikipedia-org-3337	368	489	from	from	IN
en-wikipedia-org-3337	368	490	"	"	``
en-wikipedia-org-3337	368	491	https://en.wikipedia.org/w/index.php?title=Nash_equilibrium&oldid=992436119	https://en.wikipedia.org/w/index.php?title=nash_equilibrium&oldid=992436119	JJ
en-wikipedia-org-3337	368	492	"	"	''
en-wikipedia-org-3337	368	493	Categories	category	NNS
en-wikipedia-org-3337	368	494	:	:	:
en-wikipedia-org-3337	368	495	Game	game	NN
en-wikipedia-org-3337	368	496	theory	theory	NN
en-wikipedia-org-3337	368	497	equilibrium	equilibrium	NN
en-wikipedia-org-3337	368	498	concepts	concept	VBZ
en-wikipedia-org-3337	368	499	Fixed	fix	VBN
en-wikipedia-org-3337	368	500	points	point	NNS
en-wikipedia-org-3337	368	501	(	(	-LRB-
en-wikipedia-org-3337	368	502	mathematics	mathematic	NNS
en-wikipedia-org-3337	368	503	)	)	-RRB-
en-wikipedia-org-3337	368	504	1951	1951	CD
en-wikipedia-org-3337	368	505	in	in	IN
en-wikipedia-org-3337	368	506	economics	economic	NNS
en-wikipedia-org-3337	368	507	Hidden	hide	VBN
en-wikipedia-org-3337	368	508	categories	category	NNS
en-wikipedia-org-3337	368	509	:	:	:
en-wikipedia-org-3337	368	510	All	all	DT
en-wikipedia-org-3337	368	511	articles	article	NNS
en-wikipedia-org-3337	368	512	with	with	IN
en-wikipedia-org-3337	368	513	unsourced	unsourced	JJ
en-wikipedia-org-3337	368	514	statements	statement	NNS
en-wikipedia-org-3337	368	515	Articles	article	NNS
en-wikipedia-org-3337	368	516	with	with	IN
en-wikipedia-org-3337	368	517	unsourced	unsourced	JJ
en-wikipedia-org-3337	368	518	statements	statement	NNS
en-wikipedia-org-3337	368	519	from	from	IN
en-wikipedia-org-3337	368	520	April	April	NNP
en-wikipedia-org-3337	368	521	2010	2010	CD
en-wikipedia-org-3337	368	522	Webarchive	Webarchive	NNP
en-wikipedia-org-3337	368	523	template	template	NN
en-wikipedia-org-3337	368	524	wayback	wayback	NN
en-wikipedia-org-3337	368	525	links	link	NNS
en-wikipedia-org-3337	368	526	Articles	article	NNS
en-wikipedia-org-3337	368	527	with	with	IN
en-wikipedia-org-3337	368	528	short	short	JJ
en-wikipedia-org-3337	368	529	description	description	NN
en-wikipedia-org-3337	368	530	Short	short	JJ
en-wikipedia-org-3337	368	531	description	description	NN
en-wikipedia-org-3337	368	532	is	be	VBZ
en-wikipedia-org-3337	368	533	different	different	JJ
en-wikipedia-org-3337	368	534	from	from	IN
en-wikipedia-org-3337	368	535	Wikidata	Wikidata	NNP
en-wikipedia-org-3337	368	536	Articles	Articles	NNPS
en-wikipedia-org-3337	368	537	with	with	IN
en-wikipedia-org-3337	368	538	unsourced	unsourced	JJ
en-wikipedia-org-3337	368	539	statements	statement	NNS
en-wikipedia-org-3337	368	540	from	from	IN
en-wikipedia-org-3337	368	541	June	June	NNP
en-wikipedia-org-3337	368	542	2012	2012	CD
en-wikipedia-org-3337	368	543	Navigation	Navigation	NNP
en-wikipedia-org-3337	368	544	menu	menu	NN
en-wikipedia-org-3337	368	545	Personal	personal	JJ
en-wikipedia-org-3337	368	546	tools	tool	NNS
en-wikipedia-org-3337	368	547	Not	not	RB
en-wikipedia-org-3337	368	548	logged	log	VBN
en-wikipedia-org-3337	368	549	in	in	IN
en-wikipedia-org-3337	368	550	Talk	Talk	NNP
en-wikipedia-org-3337	368	551	Contributions	Contributions	NNP
en-wikipedia-org-3337	368	552	Create	Create	NNP
en-wikipedia-org-3337	368	553	account	account	NN
en-wikipedia-org-3337	368	554	Log	Log	NNP
en-wikipedia-org-3337	368	555	in	in	IN
en-wikipedia-org-3337	368	556	Namespaces	Namespaces	NNP
en-wikipedia-org-3337	368	557	Article	Article	NNP
en-wikipedia-org-3337	368	558	Talk	talk	NN
en-wikipedia-org-3337	368	559	Variants	variant	VBZ
en-wikipedia-org-3337	368	560	Views	view	NNS
en-wikipedia-org-3337	368	561	Read	read	VBP
en-wikipedia-org-3337	368	562	Edit	edit	NN
en-wikipedia-org-3337	368	563	View	View	NNP
en-wikipedia-org-3337	368	564	history	history	NN
en-wikipedia-org-3337	368	565	More	More	JJR
en-wikipedia-org-3337	368	566	Search	Search	NNP
en-wikipedia-org-3337	368	567	Navigation	Navigation	NNP
en-wikipedia-org-3337	368	568	Main	Main	NNP
en-wikipedia-org-3337	368	569	page	page	NN
en-wikipedia-org-3337	368	570	Contents	content	VBZ
en-wikipedia-org-3337	368	571	Current	current	JJ
en-wikipedia-org-3337	368	572	events	event	NNS
en-wikipedia-org-3337	368	573	Random	random	JJ
en-wikipedia-org-3337	368	574	article	article	NN
en-wikipedia-org-3337	368	575	About	about	IN
en-wikipedia-org-3337	368	576	Wikipedia	Wikipedia	NNP
en-wikipedia-org-3337	368	577	Contact	Contact	NNP
en-wikipedia-org-3337	368	578	us	-PRON-	PRP
en-wikipedia-org-3337	368	579	Donate	Donate	NNP
en-wikipedia-org-3337	368	580	Contribute	contribute	NN
en-wikipedia-org-3337	368	581	Help	help	NN
en-wikipedia-org-3337	368	582	Learn	learn	VB
en-wikipedia-org-3337	368	583	to	to	TO
en-wikipedia-org-3337	368	584	edit	edit	VB
en-wikipedia-org-3337	368	585	Community	community	NN
en-wikipedia-org-3337	368	586	portal	portal	JJ
en-wikipedia-org-3337	368	587	Recent	recent	JJ
en-wikipedia-org-3337	368	588	changes	change	NNS
en-wikipedia-org-3337	368	589	Upload	upload	JJ
en-wikipedia-org-3337	368	590	file	file	NN
en-wikipedia-org-3337	368	591	Tools	tool	NNS
en-wikipedia-org-3337	368	592	What	what	WP
en-wikipedia-org-3337	368	593	links	link	NNS
en-wikipedia-org-3337	368	594	here	here	RB
en-wikipedia-org-3337	368	595	Related	relate	VBN
en-wikipedia-org-3337	368	596	changes	change	VBZ
en-wikipedia-org-3337	368	597	Upload	upload	JJ
en-wikipedia-org-3337	368	598	file	file	VBP
en-wikipedia-org-3337	368	599	Special	special	JJ
en-wikipedia-org-3337	368	600	pages	page	NNS
en-wikipedia-org-3337	368	601	Permanent	permanent	JJ
en-wikipedia-org-3337	368	602	link	link	NN
en-wikipedia-org-3337	368	603	Page	Page	NNP
en-wikipedia-org-3337	368	604	information	information	NN
en-wikipedia-org-3337	368	605	Cite	cite	VB
en-wikipedia-org-3337	368	606	this	this	DT
en-wikipedia-org-3337	368	607	page	page	NN
en-wikipedia-org-3337	368	608	Wikidata	wikidata	NN
en-wikipedia-org-3337	368	609	item	item	NN
en-wikipedia-org-3337	368	610	Print	print	NN
en-wikipedia-org-3337	368	611	/	/	SYM
en-wikipedia-org-3337	368	612	export	export	NN
en-wikipedia-org-3337	368	613	Download	Download	NNP
en-wikipedia-org-3337	368	614	as	as	IN
en-wikipedia-org-3337	368	615	PDF	PDF	NNP
en-wikipedia-org-3337	368	616	Printable	Printable	NNP
en-wikipedia-org-3337	368	617	version	version	NN
en-wikipedia-org-3337	368	618	In	in	IN
en-wikipedia-org-3337	368	619	other	other	JJ
en-wikipedia-org-3337	368	620	projects	project	NNS
en-wikipedia-org-3337	368	621	Wikiquote	Wikiquote	NNP
en-wikipedia-org-3337	368	622	Languages	Languages	NNP
en-wikipedia-org-3337	368	623	العربية	العربية	NN
en-wikipedia-org-3337	368	624	অসমীয়া	অসমীয়া	.
en-wikipedia-org-3337	368	625	Azərbaycanca	Azərbaycanca	NNP
en-wikipedia-org-3337	368	626	Български	Български	NNP
en-wikipedia-org-3337	368	627	Català	Català	NNP
en-wikipedia-org-3337	368	628	Čeština	Čeština	NNP
en-wikipedia-org-3337	368	629	Dansk	Dansk	NNP
en-wikipedia-org-3337	368	630	Deutsch	Deutsch	NNP
en-wikipedia-org-3337	368	631	Eesti	Eesti	NNP
en-wikipedia-org-3337	368	632	Ελληνικά	Ελληνικά	NNP
en-wikipedia-org-3337	368	633	Español	Español	NNP
en-wikipedia-org-3337	368	634	Esperanto	Esperanto	NNP
en-wikipedia-org-3337	368	635	Euskara	Euskara	NNP
en-wikipedia-org-3337	368	636	فارسی	فارسی	JJ
en-wikipedia-org-3337	368	637	Français	Français	NNP
en-wikipedia-org-3337	368	638	Galego	Galego	NNP
en-wikipedia-org-3337	368	639	한국어	한국어	NN
en-wikipedia-org-3337	368	640	हिन्दी	हिन्दी	NNP
en-wikipedia-org-3337	368	641	Íslenska	Íslenska	NNP
en-wikipedia-org-3337	368	642	Italiano	Italiano	NNP
en-wikipedia-org-3337	368	643	עברית	עברית	NN
en-wikipedia-org-3337	368	644	Lietuvių	Lietuvių	NNP
en-wikipedia-org-3337	368	645	Magyar	Magyar	NNP
en-wikipedia-org-3337	368	646	Монгол	Монгол	NNP
en-wikipedia-org-3337	368	647	Nederlands	Nederlands	NNP
en-wikipedia-org-3337	368	648	日本語	日本語	NNP
en-wikipedia-org-3337	368	649	Norsk	Norsk	NNP
en-wikipedia-org-3337	368	650	bokmål	bokmål	NN
en-wikipedia-org-3337	368	651	Norsk	Norsk	NNP
en-wikipedia-org-3337	368	652	nynorsk	nynorsk	NNP
en-wikipedia-org-3337	368	653	پښتو	پښتو	NNP
en-wikipedia-org-3337	368	654	Polski	Polski	NNP
en-wikipedia-org-3337	368	655	Português	Português	NNP
en-wikipedia-org-3337	368	656	Română	Română	NNP
en-wikipedia-org-3337	368	657	Русский	Русский	NNP
en-wikipedia-org-3337	368	658	Sicilianu	Sicilianu	NNP
en-wikipedia-org-3337	368	659	Simple	Simple	NNP
en-wikipedia-org-3337	368	660	English	English	NNP
en-wikipedia-org-3337	368	661	Slovenčina	Slovenčina	NNP
en-wikipedia-org-3337	368	662	Српски	Српски	NNP
en-wikipedia-org-3337	368	663	/	/	SYM
en-wikipedia-org-3337	368	664	srpski	srpski	JJ
en-wikipedia-org-3337	368	665	Srpskohrvatski	Srpskohrvatski	NNP
en-wikipedia-org-3337	368	666	/	/	SYM
en-wikipedia-org-3337	368	667	српскохрватски	српскохрватски	NN
en-wikipedia-org-3337	368	668	Suomi	Suomi	NNP
en-wikipedia-org-3337	368	669	Svenska	Svenska	NNP
en-wikipedia-org-3337	368	670	ไทย	ไทย	NN
en-wikipedia-org-3337	368	671	Türkçe	Türkçe	NNP
en-wikipedia-org-3337	368	672	Українська	Українська	NNP
en-wikipedia-org-3337	368	673	Tiếng	Tiếng	NNP
en-wikipedia-org-3337	368	674	Việt	Việt	NNP
en-wikipedia-org-3337	368	675	粵語	粵語	NNP
en-wikipedia-org-3337	368	676	中文	中文	NNP
en-wikipedia-org-3337	368	677	Edit	Edit	NNP
en-wikipedia-org-3337	368	678	links	link	NNS
en-wikipedia-org-3337	368	679	This	this	DT
en-wikipedia-org-3337	368	680	page	page	NN
en-wikipedia-org-3337	368	681	was	be	VBD
en-wikipedia-org-3337	368	682	last	last	RB
en-wikipedia-org-3337	368	683	edited	edit	VBN
en-wikipedia-org-3337	368	684	on	on	IN
en-wikipedia-org-3337	368	685	5	5	CD
en-wikipedia-org-3337	368	686	December	December	NNP
en-wikipedia-org-3337	368	687	2020	2020	CD
en-wikipedia-org-3337	368	688	,	,	,
en-wikipedia-org-3337	368	689	at	at	IN
en-wikipedia-org-3337	368	690	07:24	07:24	CD
en-wikipedia-org-3337	368	691	 	  	_SP
en-wikipedia-org-3337	368	692	(	(	-LRB-
en-wikipedia-org-3337	368	693	UTC	UTC	NNP
en-wikipedia-org-3337	368	694	)	)	-RRB-
en-wikipedia-org-3337	368	695	.	.	.
en-wikipedia-org-3337	369	1	Text	text	NN
en-wikipedia-org-3337	369	2	is	be	VBZ
en-wikipedia-org-3337	369	3	available	available	JJ
en-wikipedia-org-3337	369	4	under	under	IN
en-wikipedia-org-3337	369	5	the	the	DT
en-wikipedia-org-3337	369	6	Creative	Creative	NNP
en-wikipedia-org-3337	369	7	Commons	Commons	NNP
en-wikipedia-org-3337	369	8	Attribution	Attribution	NNP
en-wikipedia-org-3337	369	9	-	-	HYPH
en-wikipedia-org-3337	369	10	ShareAlike	ShareAlike	NNP
en-wikipedia-org-3337	369	11	License	License	NNP
en-wikipedia-org-3337	369	12	;	;	,
en-wikipedia-org-3337	369	13	additional	additional	JJ
en-wikipedia-org-3337	369	14	terms	term	NNS
en-wikipedia-org-3337	369	15	may	may	MD
en-wikipedia-org-3337	369	16	apply	apply	VB
en-wikipedia-org-3337	369	17	.	.	.
en-wikipedia-org-3337	370	1	By	by	IN
en-wikipedia-org-3337	370	2	using	use	VBG
en-wikipedia-org-3337	370	3	this	this	DT
en-wikipedia-org-3337	370	4	site	site	NN
en-wikipedia-org-3337	370	5	,	,	,
en-wikipedia-org-3337	370	6	you	-PRON-	PRP
en-wikipedia-org-3337	370	7	agree	agree	VBP
en-wikipedia-org-3337	370	8	to	to	IN
en-wikipedia-org-3337	370	9	the	the	DT
en-wikipedia-org-3337	370	10	Terms	term	NNS
en-wikipedia-org-3337	370	11	of	of	IN
en-wikipedia-org-3337	370	12	Use	Use	NNP
en-wikipedia-org-3337	370	13	and	and	CC
en-wikipedia-org-3337	370	14	Privacy	Privacy	NNP
en-wikipedia-org-3337	370	15	Policy	Policy	NNP
en-wikipedia-org-3337	370	16	.	.	.
en-wikipedia-org-3337	371	1	Wikipedia	Wikipedia	NNP
en-wikipedia-org-3337	371	2	®	®	NNPS
en-wikipedia-org-3337	371	3	is	be	VBZ
en-wikipedia-org-3337	371	4	a	a	DT
en-wikipedia-org-3337	371	5	registered	registered	JJ
en-wikipedia-org-3337	371	6	trademark	trademark	NN
en-wikipedia-org-3337	371	7	of	of	IN
en-wikipedia-org-3337	371	8	the	the	DT
en-wikipedia-org-3337	371	9	Wikimedia	Wikimedia	NNP
en-wikipedia-org-3337	371	10	Foundation	Foundation	NNP
en-wikipedia-org-3337	371	11	,	,	,
en-wikipedia-org-3337	371	12	Inc.	Inc.	NNP
en-wikipedia-org-3337	371	13	,	,	,
en-wikipedia-org-3337	371	14	a	a	DT
en-wikipedia-org-3337	371	15	non	non	JJ
en-wikipedia-org-3337	371	16	-	-	JJ
en-wikipedia-org-3337	371	17	profit	profit	JJ
en-wikipedia-org-3337	371	18	organization	organization	NN
en-wikipedia-org-3337	371	19	.	.	.
en-wikipedia-org-3337	372	1	Privacy	privacy	NN
en-wikipedia-org-3337	372	2	policy	policy	NN
en-wikipedia-org-3337	372	3	About	about	IN
en-wikipedia-org-3337	372	4	Wikipedia	Wikipedia	NNP
en-wikipedia-org-3337	372	5	Disclaimers	Disclaimers	NNPS
en-wikipedia-org-3337	372	6	Contact	Contact	NNP
en-wikipedia-org-3337	372	7	Wikipedia	Wikipedia	NNP
en-wikipedia-org-3337	372	8	Mobile	Mobile	NNP
en-wikipedia-org-3337	372	9	view	view	NN
en-wikipedia-org-3337	372	10	Developers	Developers	NNP
en-wikipedia-org-3337	372	11	Statistics	Statistics	NNP
en-wikipedia-org-3337	372	12	Cookie	Cookie	NNP
en-wikipedia-org-3337	372	13	statement	statement	NN