Pareto efficiency - Wikipedia Pareto efficiency From Wikipedia, the free encyclopedia Jump to navigation Jump to search State in which no reallocation of resources can make everyone at least as well off This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Pareto efficiency" – news · newspapers · books · scholar · JSTOR (November 2020) (Learn how and when to remove this template message) Pareto efficiency or Pareto optimality is a situation where no individual or preference criterion can be better off without making at least one individual or preference criterion worse off or without any loss thereof. The concept is named after Vilfredo Pareto (1848–1923), Italian engineer and economist, who used the concept in his studies of economic efficiency and income distribution. The following three concepts are closely related: Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. A situation is called Pareto dominated if there exists a possible Pareto improvement. A situation is called Pareto optimal or Pareto efficient if no change could lead to improved satisfaction for some agent without some other agent losing or if there's no scope for further Pareto improvement. The Pareto frontier is the set of all Pareto efficient allocations, conventionally shown graphically. It also is variously known as the Pareto front or Pareto set.[1] Pareto originally used the word "optimal" for the concept, but as it describes a situation where a limited number of people will be made better off under finite resources, and it does not take equality or social well-being into account, it is in effect a definition of and better captured by "efficiency".[2] In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.[3]:459 Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in engineering and biology. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of multi-objective optimization (also termed Pareto optimization). Contents 1 Overview 2 Weak Pareto efficiency 3 Constrained Pareto efficiency 4 Fractional Pareto efficiency 5 Pareto-efficiency and welfare-maximization 6 Use in engineering 6.1 Pareto frontier 6.2 Marginal rate of substitution 6.3 Computation 7 Use in public policy 8 Use in biology 9 Common misconceptions 10 Criticism 11 See also 12 References 13 Further reading Overview[edit] Formally, an allocation is Pareto optimal if there is no alternative allocation where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a transfer that satisfies this condition, the new reallocation is called a "Pareto improvement". When no Pareto improvements are possible, the allocation is a "Pareto optimum". The formal presentation of the concept in an economy is the following: Consider an economy with n {\displaystyle n} agents and k {\displaystyle k} goods. Then an allocation { x 1 , . . . , x n } {\displaystyle \{x_{1},...,x_{n}\}} , where x i ∈ R k {\displaystyle x_{i}\in \mathbb {R} ^{k}} for all i, is Pareto optimal if there is no other feasible allocation { x 1 ′ , . . . , x n ′ } {\displaystyle \{x_{1}',...,x_{n}'\}} where, for utility function u i {\displaystyle u_{i}} for each agent i {\displaystyle i} , u i ( x i ′ ) ≥ u i ( x i ) {\displaystyle u_{i}(x_{i}')\geq u_{i}(x_{i})} for all i ∈ { 1 , . . . , n } {\displaystyle i\in \{1,...,n\}} with u i ( x i ′ ) > u i ( x i ) {\displaystyle u_{i}(x_{i}')>u_{i}(x_{i})} for some i {\displaystyle i} .[4] Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced. Under the assumptions of the first welfare theorem, a competitive market leads to a Pareto-efficient outcome. This result was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu.[5][citation needed] However, the result only holds under the assumptions of the theorem: markets exist for all possible goods, there are no externalities; markets are perfectly competitive; and market participants have perfect information. In the absence of perfect information or complete markets, outcomes will generally be Pareto inefficient, per the Greenwald-Stiglitz theorem.[6] The second welfare theorem is essentially the reverse of the first welfare-theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some competitive equilibrium, or free market system, although it may also require a lump-sum transfer of wealth.[4] Weak Pareto efficiency[edit] Weak Pareto optimality is a situation that cannot be strictly improved for every individual.[7] Formally, a strong Pareto improvement is defined as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is weak Pareto-optimal if it has no strong Pareto-improvements. Any strong Pareto-improvement is also a weak Pareto-improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at 10, 0 and George values at 5, 5. Consider the allocation giving all resources to Alice, where the utility profile is (10,0): It is a weak-PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements). But it is not a strong-PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) - its utility profile is (10,5). A market doesn't require local nonsatiation to get to a weak Pareto-optimum.[8] Constrained Pareto efficiency [edit] Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.[9]:104 An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in moral hazard or an adverse selection and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type A, they pay price p1, but if of type B, they pay price p2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price p") or rules based on observable behavior; "if any person chooses x at price px, then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal". Fractional Pareto efficiency[edit] Fractional Pareto optimality is a strengthening of Pareto-optimality in the context of fair item allocation. An allocation of indivisible items is fractionally Pareto-optimal (fPO) if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto-optimality, which only considers domination by feasible (discrete) allocations.[10] As an example, consider an item allocation problem with two items, which Alice values at 3, 2 and George values at 4, 1. Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3,1): It is Pareto-optimal, since any other discrete allocation (without splitting items) makes someone worse-off. However, it is not fractionally-Pareto-optimal, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George - its utility profile is (3.5, 2). Pareto-efficiency and welfare-maximization[edit] See also: Pareto-efficient envy-free division Suppose each agent i is assigned a positive weight ai. For every allocation x, define the welfare of x as the weighted sum of utilities of all agents in x, i.e.: W a ( x ) := ∑ i = 1 n a i u i ( x ) {\displaystyle W_{a}(x):=\sum _{i=1}^{n}a_{i}u_{i}(x)} . Let xa be an allocation that maximizes the welfare over all allocations, i.e.: x a ∈ arg ⁡ max x W a ( x ) {\displaystyle x_{a}\in \arg \max _{x}W_{a}(x)} . It is easy to show that the allocation xa is Pareto-efficient: since all weights are positive, any Pareto-improvement would increase the sum, contradicting the definition of xa. Japanese neo-Walrasian economist Takashi Negishi proved[11] that, under certain assumptions, the opposite is also true: for every Pareto-efficient allocation x, there exists a positive vector a such that x maximizes Wa. A shorter proof is provided by Hal Varian.[12] Use in engineering[edit] The notion of Pareto efficiency has been used in engineering.[13]:111–148 Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.[14]:63–65 Example of a Pareto frontier. The boxed points represent feasible choices, and smaller values are preferred to larger ones. Point C is not on the Pareto frontier because it is dominated by both point A and point B. Points A and B are not strictly dominated by any other, and hence lie on the frontier. A production-possibility frontier. The red line is an example of a Pareto-efficient frontier, where the frontier and the area left and below it are a continuous set of choices. The red points on the frontier are examples of Pareto-optimal choices of production. Points off the frontier, such as N and K, are not Pareto-efficient, since there exist points on the frontier which Pareto-dominate them. Pareto frontier[edit] For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.[15]:399–412 The Pareto frontier, P(Y), may be more formally described as follows. Consider a system with function f : X → R m {\displaystyle f:X\rightarrow \mathbb {R} ^{m}} , where X is a compact set of feasible decisions in the metric space R n {\displaystyle \mathbb {R} ^{n}} , and Y is the feasible set of criterion vectors in R m {\displaystyle \mathbb {R} ^{m}} , such that Y = { y ∈ R m : y = f ( x ) , x ∈ X } {\displaystyle Y=\{y\in \mathbb {R} ^{m}:\;y=f(x),x\in X\;\}} . We assume that the preferred directions of criteria values are known. A point y ′ ′ ∈ R m {\displaystyle y^{\prime \prime }\in \mathbb {R} ^{m}} is preferred to (strictly dominates) another point y ′ ∈ R m {\displaystyle y^{\prime }\in \mathbb {R} ^{m}} , written as y ′ ′ ≻ y ′ {\displaystyle y^{\prime \prime }\succ y^{\prime }} . The Pareto frontier is thus written as: P ( Y ) = { y ′ ∈ Y : { y ′ ′ ∈ Y : y ′ ′ ≻ y ′ , y ′ ≠ y ′ ′ } = ∅ } . {\displaystyle P(Y)=\{y^{\prime }\in Y:\;\{y^{\prime \prime }\in Y:\;y^{\prime \prime }\succ y^{\prime },y^{\prime }\neq y^{\prime \prime }\;\}=\emptyset \}.} Marginal rate of substitution[edit] A significant aspect of the Pareto frontier in economics is that, at a Pareto-efficient allocation, the marginal rate of substitution is the same for all consumers.[16] A formal statement can be derived by considering a system with m consumers and n goods, and a utility function of each consumer as z i = f i ( x i ) {\displaystyle z_{i}=f^{i}(x^{i})} where x i = ( x 1 i , x 2 i , … , x n i ) {\displaystyle x^{i}=(x_{1}^{i},x_{2}^{i},\ldots ,x_{n}^{i})} is the vector of goods, both for all i. The feasibility constraint is ∑ i = 1 m x j i = b j {\displaystyle \sum _{i=1}^{m}x_{j}^{i}=b_{j}} for j = 1 , … , n {\displaystyle j=1,\ldots ,n} . To find the Pareto optimal allocation, we maximize the Lagrangian: L i ( ( x j k ) k , j , ( λ k ) k , ( μ j ) j ) = f i ( x i ) + ∑ k = 2 m λ k ( z k − f k ( x k ) ) + ∑ j = 1 n μ j ( b j − ∑ k = 1 m x j k ) {\displaystyle L_{i}((x_{j}^{k})_{k,j},(\lambda _{k})_{k},(\mu _{j})_{j})=f^{i}(x^{i})+\sum _{k=2}^{m}\lambda _{k}(z_{k}-f^{k}(x^{k}))+\sum _{j=1}^{n}\mu _{j}\left(b_{j}-\sum _{k=1}^{m}x_{j}^{k}\right)} where ( λ k ) k {\displaystyle (\lambda _{k})_{k}} and ( μ j ) j {\displaystyle (\mu _{j})_{j}} are the vectors of multipliers. Taking the partial derivative of the Lagrangian with respect to each good x j k {\displaystyle x_{j}^{k}} for j = 1 , … , n {\displaystyle j=1,\ldots ,n} and k = 1 , … , m {\displaystyle k=1,\ldots ,m} and gives the following system of first-order conditions: ∂ L i ∂ x j i = f x j i 1 − μ j = 0  for  j = 1 , … , n , {\displaystyle {\frac {\partial L_{i}}{\partial x_{j}^{i}}}=f_{x_{j}^{i}}^{1}-\mu _{j}=0{\text{ for }}j=1,\ldots ,n,} ∂ L i ∂ x j k = − λ k f x j k i − μ j = 0  for  k = 2 , … , m  and  j = 1 , … , n , {\displaystyle {\frac {\partial L_{i}}{\partial x_{j}^{k}}}=-\lambda _{k}f_{x_{j}^{k}}^{i}-\mu _{j}=0{\text{ for }}k=2,\ldots ,m{\text{ and }}j=1,\ldots ,n,} where f x j i {\displaystyle f_{x_{j}^{i}}} denotes the partial derivative of f {\displaystyle f} with respect to x j i {\displaystyle x_{j}^{i}} . Now, fix any k ≠ i {\displaystyle k\neq i} and j , s ∈ { 1 , … , n } {\displaystyle j,s\in \{1,\ldots ,n\}} . The above first-order condition imply that f x j i i f x s i i = μ j μ s = f x j k k f x s k k . {\displaystyle {\frac {f_{x_{j}^{i}}^{i}}{f_{x_{s}^{i}}^{i}}}={\frac {\mu _{j}}{\mu _{s}}}={\frac {f_{x_{j}^{k}}^{k}}{f_{x_{s}^{k}}^{k}}}.} Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.[citation needed] Computation[edit] Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied in computer science and power engineering.[17] They include: "The maximum vector problem" or the skyline query.[18][19][20] "The scalarization algorithm" or the method of weighted sums.[21][22] "The ϵ {\displaystyle \epsilon } -constraints method".[23][24] Use in public policy[edit] The modern microeconomic theory drew inspirations heavily from Pareto efficiency. Since Pareto showed that the equilibrium achieved through competition would optimize resource allocation, it is effectively corroborating Adam Smith's "invisible hand" notion. More specifically, it motivated the debate over "market socialism" in the 1930s. [25] Use in biology[edit] Pareto optimisation has also been studied in biological processes.[26]:87–102 In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency.[27]:166–169 Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).[28] Common misconceptions[edit] It would be incorrect to treat Pareto efficiency as equivalent to societal optimization,[29]:358–364 as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution.[30]:10–15 An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.[31]:95–132 Criticism[edit] This section will introduce criticisms from the most radical to more moderate ones. Some commentators contest that Pareto efficiency could potentially serve as an ideological tool. With it implying that capitalism is self-regulated thereof, it is likely that the embedded structural problems such as unemployment would be treated as deviating from the equilibrium or norm, and thus neglected or discounted. [32] Pareto efficiency does not require a totally equitable distribution of wealth, which is another aspect that draws in criticism.[33]:222 An economy in which a wealthy few hold the vast majority of resources can be Pareto efficient. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded.[34]:18 The liberal paradox elaborated by Amartya Sen shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.[35]:92–94 Lastly, it is proposed that Pareto efficiency to some extent inhibited discussion of other possible criteria of efficiency. As the scholar Lockhood argues, one possible reason is that any other efficiency criteria established in the neoclassical domain will reduce to Pareto efficiency at the end. [36] See also[edit] Admissible decision rule, analog in decision theory Arrow's impossibility theorem Bayesian efficiency Fundamental theorems of welfare economics Deadweight loss Economic efficiency Highest and best use Kaldor–Hicks efficiency Market failure, when a market result is not Pareto optimal Maximal element, concept in order theory Maxima of a point set Multi-objective optimization Pareto-efficient envy-free division Social Choice and Individual Values for the '(weak) Pareto principle' TOTREP Welfare economics References[edit] ^ proximedia. "Pareto Front". www.cenaero.be. Retrieved October 8, 2018. ^ Lockwood, B. (2008). The New Palgrave Dictionary of Economics (2nd ed.). London: Palgrave Macmillan. ISBN 978-1-349-95121-5. ^ Black, J. D., Hashimzade, N., & Myles, G., eds., A Dictionary of Economics, 5th ed. (Oxford: Oxford University Press, 2017), p. 459. ^ a b Mas-Colell, A.; Whinston, Michael D.; Green, Jerry R. (1995), "Chapter 16: Equilibrium and its Basic Welfare Properties", Microeconomic Theory, Oxford University Press, ISBN 978-0-19-510268-0 ^ Gerard, Debreu (1959). "VALUATION EQUILIBRIUM AND PARETO OPTIMUM*". Proceedings of the National Academy of Sciences of the United States of America. 40 (7): 588–592. doi:10.1073/pnas.40.7.588. ^ Greenwald, B.; Stiglitz, J. E. (1986). "Externalities in economies with imperfect information and incomplete markets". Quarterly Journal of Economics. 101 (2): 229–64. doi:10.2307/1891114. JSTOR 1891114. ^ Mock, William B T. (2011). "Pareto Optimality". Encyclopedia of Global Justice. pp. 808–809. doi:10.1007/978-1-4020-9160-5_341. ISBN 978-1-4020-9159-9. ^ Markey‐Towler, Brendan and John Foster. "Why economic theory has little to say about the causes and effects of inequality", School of Economics, University of Queensland, Australia, 21 February 2013, RePEc:qld:uq2004:476 ^ Magill, M., & Quinzii, M., Theory of Incomplete Markets, MIT Press, 2002, p. 104. ^ Barman, S., Krishnamurthy, S. K., & Vaish, R., "Finding Fair and Efficient Allocations", EC '18: Proceedings of the 2018 ACM Conference on Economics and Computation, June 2018. ^ Negishi, Takashi (1960). "Welfare Economics and Existence of an Equilibrium for a Competitive Economy". Metroeconomica. 12 (2–3): 92–97. doi:10.1111/j.1467-999X.1960.tb00275.x. ^ Varian, Hal R. (1976). "Two problems in the theory of fairness". Journal of Public Economics. 5 (3–4): 249–260. doi:10.1016/0047-2727(76)90018-9. hdl:1721.1/64180. ^ Goodarzi, E., Ziaei, M., & Hosseinipour, E. Z., Introduction to Optimization Analysis in Hydrosystem Engineering (Berlin/Heidelberg: Springer, 2014), pp. 111–148. ^ Jahan, A., Edwards, K. L., & Bahraminasab, M., Multi-criteria Decision Analysis, 2nd ed. (Amsterdam: Elsevier, 2013), pp. 63–65. ^ Costa, N. R., & Lourenço, J. A., "Exploring Pareto Frontiers in the Response Surface Methodology", in G.-C. Yang, S.-I. Ao, & L. Gelman, eds., Transactions on Engineering Technologies: World Congress on Engineering 2014 (Berlin/Heidelberg: Springer, 2015), pp. 399–412. ^ Just, Richard E. (2004). The welfare economics of public policy : a practical approach to project and policy evaluation. Hueth, Darrell L., Schmitz, Andrew. Cheltenham, UK: E. Elgar. pp. 18–21. ISBN 1-84542-157-4. OCLC 58538348. ^ Tomoiagă, Bogdan; Chindriş, Mircea; Sumper, Andreas; Sudria-Andreu, Antoni; Villafafila-Robles, Roberto (2013). "Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II". Energies. 6 (3): 1439–55. doi:10.3390/en6031439. ^ Nielsen, Frank (1996). "Output-sensitive peeling of convex and maximal layers". Information Processing Letters. 59 (5): 255–9. CiteSeerX 10.1.1.259.1042. doi:10.1016/0020-0190(96)00116-0. ^ Kung, H. T.; Luccio, F.; Preparata, F.P. (1975). "On finding the maxima of a set of vectors". Journal of the ACM. 22 (4): 469–76. doi:10.1145/321906.321910. S2CID 2698043. ^ Godfrey, P.; Shipley, R.; Gryz, J. (2006). "Algorithms and Analyses for Maximal Vector Computation". VLDB Journal. 16: 5–28. CiteSeerX 10.1.1.73.6344. doi:10.1007/s00778-006-0029-7. S2CID 7374749. ^ Kim, I. Y.; de Weck, O. L. (2005). "Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation". Structural and Multidisciplinary Optimization. 31 (2): 105–116. doi:10.1007/s00158-005-0557-6. ISSN 1615-147X. S2CID 18237050. ^ Marler, R. Timothy; Arora, Jasbir S. (2009). "The weighted sum method for multi-objective optimization: new insights". Structural and Multidisciplinary Optimization. 41 (6): 853–862. doi:10.1007/s00158-009-0460-7. ISSN 1615-147X. S2CID 122325484. ^ "On a Bicriterion Formulation of the Problems of Integrated System Identification and System Optimization". IEEE Transactions on Systems, Man, and Cybernetics. SMC-1 (3): 296–297. 1971. doi:10.1109/TSMC.1971.4308298. ISSN 0018-9472. ^ Mavrotas, George (2009). "Effective implementation of the ε-constraint method in Multi-Objective Mathematical Programming problems". Applied Mathematics and Computation. 213 (2): 455–465. doi:10.1016/j.amc.2009.03.037. ISSN 0096-3003. ^ Lockwood, B. (2008). The New Palgrave Dictionary of Economics (2nd ed.). London: Palgrave Macmillan. ISBN 978-1-349-95121-5. ^ Moore, J. H., Hill, D. P., Sulovari, A., & Kidd, L. C., "Genetic Analysis of Prostate Cancer Using Computational Evolution, Pareto-Optimization and Post-processing", in R. Riolo, E. Vladislavleva, M. D. Ritchie, & J. H. Moore, eds., Genetic Programming Theory and Practice X (Berlin/Heidelberg: Springer, 2013), pp. 87–102. ^ Eiben, A. E., & Smith, J. E., Introduction to Evolutionary Computing (Berlin/Heidelberg: Springer, 2003), pp. 166–169. ^ Seward, E. A., & Kelly, S., "Selection-driven cost-efficiency optimization of transcripts modulates gene evolutionary rate in bacteria", Genome Biology, Vol. 19, 2018. ^ Drèze, J., Essays on Economic Decisions Under Uncertainty (Cambridge: Cambridge University Press, 1987), pp. 358–364 ^ Backhaus, J. G., The Elgar Companion to Law and Economics (Cheltenham, UK / Northampton, MA: Edward Elgar, 2005), pp. 10–15. ^ Paulsen, M. B., "The Economics of the Public Sector: The Nature and Role of Public Policy in the Finance of Higher Education", in M. B. Paulsen, J. C. Smart, eds. The Finance of Higher Education: Theory, Research, Policy, and Practice (New York: Agathon Press, 2001), pp. 95–132. ^ Lockwood, B. (2008). The New Palgrave Dictionary of Economics (2nd ed.). London: Palgrave Macmillan. ISBN 978-1-349-95121-5. ^ Bhushi, K., ed., Farm to Fingers: The Culture and Politics of Food in Contemporary India (Cambridge: Cambridge University Press, 2018), p. 222. ^ Wittman, D., Economic Foundations of Law and Organization (Cambridge: Cambridge University Press, 2006), p. 18. ^ Sen, A., Rationality and Freedom (Cambridge, MA / London: Belknep Press, 2004), pp. 92–94. ^ Lockwood, B. (2008). The New Palgrave Dictionary of Economics (2nd ed.). London: Palgrave Macmillan. ISBN 978-1-349-95121-5. Further reading[edit] Fudenberg, Drew; Tirole, Jean (1991). Game theory. Cambridge, Massachusetts: MIT Press. pp. 18–23. ISBN 9780262061414. Book preview. Bendor, Jonathan; Mookherjee, Dilip (April 2008). "Communitarian versus Universalistic norms". Quarterly Journal of Political Science. 3 (1): 33–61. doi:10.1561/100.00007028.CS1 maint: ref=harv (link) Kanbur, Ravi (January–June 2005). "Pareto's revenge" (PDF). Journal of Social and Economic Development. 7 (1): 1–11.CS1 maint: ref=harv (link) Ng, Yew-Kwang (2004). Welfare economics towards a more complete analysis. Basingstoke, Hampshire New York: Palgrave Macmillan. ISBN 9780333971215. Rubinstein, Ariel; Osborne, Martin J. (1994), "Introduction", in Rubinstein, Ariel; Osborne, Martin J. (eds.), A course in game theory, Cambridge, Massachusetts: MIT Press, pp. 6–7, ISBN 9780262650403 Book preview. Mathur, Vijay K. (Spring 1991). "How well do we know Pareto optimality?". The Journal of Economic Education. 22 (2): 172–178. doi:10.2307/1182422. JSTOR 1182422.CS1 maint: ref=harv (link) Newbery, David M.G.; Stiglitz, Joseph E. (January 1984). "Pareto inferior trade". The Review of Economic Studies. 51 (1): 1–12. doi:10.2307/2297701. 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Commons Irving Fisher Wesley Clair Mitchell John Maynard Keynes Joseph Schumpeter Arthur Cecil Pigou Frank Knight John von Neumann Alvin Hansen Jacob Viner Edward Chamberlin Ragnar Frisch Harold Hotelling Michał Kalecki Oskar R. Lange Jacob Marschak Gunnar Myrdal Abba P. Lerner Roy Harrod Piero Sraffa Simon Kuznets Joan Robinson E. F. Schumacher Friedrich Hayek John Hicks Tjalling Koopmans Nicholas Georgescu-Roegen Wassily Leontief John Kenneth Galbraith Hyman Minsky Herbert A. Simon Milton Friedman Paul Samuelson Kenneth Arrow William Baumol Gary Becker Elinor Ostrom Robert Solow Amartya Sen Robert Lucas Jr. Joseph Stiglitz Richard Thaler Paul Krugman Thomas Piketty more International organizations Asia-Pacific Economic Cooperation Economic Cooperation Organization European Free Trade Association International Monetary Fund Organisation for Economic Co-operation and Development World Bank World Trade Organization Category Index Lists Outline Publications Business portal v t e Topics in game theory Definitions Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game Equilibrium concepts Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium Strategies Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy Bid shading Classes of games Symmetric game Perfect information Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game Mean field game n-player game Large Poisson game Nontransitive game Global game Strictly determined game Potential game Games Go Chess Infinite chess Checkers Tic-tac-toe Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and Monster game Rendezvous problem Theorems Arrow's impossibility theorem Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Purification theorem Revelation principle Zermelo's theorem Key figures Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey See also All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory First-move advantage in chess Game mechanics Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions v t e Electoral systems Part of the politics and election series Single-winner Approval voting Combined approval voting Unified Primary Borda count Bucklin voting Contingent vote Supplementary vote Condorcet methods Copeland's method Dodgson's method Kemeny–Young method Minimax Condorcet Nanson's method Ranked pairs Schulze method Exhaustive ballot First-past-the-post voting Instant-runoff (ranked choice) voting Coombs' method Majority judgment Simple majoritarianism Plurality Positional voting system Score voting STAR voting Two-round system Proportional CPO-STV Dual member Hare-Clark Highest averages method Webster/Sainte-Laguë D'Hondt Largest remainder method Mixed-member Party-list Schulze STV Single transferable vote Semi-proportional Parallel voting Single non-transferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting Alternative vote plus Criteria Condorcet criterion Condorcet loser criterion Consistency criterion Independence of clones Independence of irrelevant alternatives Independence of Smith-dominated alternatives Later-no-harm criterion Majority criterion Majority loser criterion Monotonicity criterion Mutual majority criterion Pareto efficiency Participation criterion Plurality criterion Resolvability criterion Reversal symmetry Smith criterion Quotas Droop quota Hagenbach-Bischoff quota Hare quota Imperiali quota Other Ballot Election threshold First-preference votes Spoilt vote Sortition Comparison Comparison of voting systems Voting systems by country Portal — Project Authority control GND: 4173334-4 Retrieved from "https://en.wikipedia.org/w/index.php?title=Pareto_efficiency&oldid=993547483" Categories: Pareto efficiency Game theory Law and economics Welfare economics Mathematical optimization Electoral system criteria Vilfredo Pareto Hidden categories: CS1: long volume value Articles with short description Short description is different from Wikidata Use mdy dates from January 2016 Articles needing additional references from November 2020 All articles needing additional references All articles with unsourced statements Articles with unsourced statements from November 2020 Articles with unsourced statements from July 2020 CS1 maint: ref=harv Wikipedia articles with GND identifiers Navigation menu Personal tools Not logged in Talk Contributions Create account Log in Namespaces Article Talk Variants Views Read Edit View history More Search Navigation Main page Contents Current events Random article About Wikipedia Contact us Donate Contribute Help Learn to edit Community portal Recent changes Upload file Tools What links here Related changes Upload file Special pages Permanent link Page information Cite this page Wikidata item Print/export Download as PDF Printable version In other projects Wikimedia Commons Languages العربية Azərbaycanca Български Català Čeština Dansk Deutsch Eesti Ελληνικά Español Esperanto Euskara فارسی Français Galego 한국어 Հայերեն Íslenska Italiano עברית Lietuvių Magyar Македонски Nederlands 日本語 Norsk bokmål Polski Português Română Русский Simple English Српски / srpski Suomi Svenska Türkçe Українська Tiếng Việt 粵語 中文 Edit links This page was last edited on 11 December 2020, at 04:47 (UTC). 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