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 FACULTY WORKING 
 PAPER NO. 90-1648 
 
 Supra-Competitive Prices and Market Power 
 in Posted-Offer Experiments 
 
 Douglas D. Davis 
 Charles A. Holt 
 Anne P. Villamil 
 
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 College of Commerce and Business Administration 
 Bureau of Economic and Business Research 
 University of Illinois Urbana-Champaign 
 
BEBR 
 
 FACULTY WORKING PAPER NO. 90-1648 
 
 College of Commerce and Business Administration 
 
 University of Illinois at Urbana-Champaign 
 
 April 1990 
 
 Supra-Competitive Prices and Market Power 
 in Posted-Offer Experiments 
 
 Douglas D. Davis 
 Virginia Commonwealth University 
 
 and 
 
 Charles A. Holt 
 University of Virginia 
 
 and 
 
 Anne P. Villamil 
 Department of Economics 
 University of Illinois, Champaign, IL 
 
 Financial assistance from the National Science Foundation (SES 87-20105 and 
 SES 89-09242) is gratefully acknowledged. 
 
ABSTRACT 
 
 This paper reports the results of a series of posted-offer market experiments designed 
 to examine the effects of static market power on prices, when other factors such as 
 excess supply, the number of sellers, and dynamic increase in posted-offer triopolies 
 with complete demand information. The effects of market power are not as obvious in 
 duopolies, since it is possible to observe considerable tacit collusion with only two 
 sellers, even in the absence of market power. 
 
Digitized by the Internet Archive 
 
 in 2011 with funding from 
 
 University of Illinois Urbana-Champaign 
 
 http://www.archive.org/details/supracompetitive1648davi 
 
Supra-Competitive Prices and Market Power in Posted-Offer Experiments 
 Douglas D. Davis, Charles A. Holt, and Anne P. Villamil* 
 
 March 1990 
 
 I. Introduction 
 
 Despite the marked tendency for prices in laboratory experiments to 
 converge to competitive predictions, laboratory sellers are sometimes able to 
 maintain prices above competitive levels. 1 A variety of factors have been 
 associated with supra-competitive prices in laboratory markets. Plott and 
 Smith (1978) showed that the rules of the market institution are important: 
 prices are higher when sellers choose prices simultaneously in a posted-offer 
 auction than when buyers and sellers make bids and offers sequentially in an 
 oral double auction. Smith (1965) attributed price deviations during an 
 adjustment phase of an oral double auction to a relatively low excess supply 
 at supra-competitive prices, and Davis and Williams (1990) offer a similar 
 conjecture about price patterns in posted-offer auctions. Dolbear et al . 
 (1968), Isaac and Reynolds (1989), Wellford (1990), and others have reported 
 that a decrease in the number of sellers tends to increase prices in several 
 distinct trading institutions. Finally, Dolbear et al . find that prices are 
 more likely to exceed noncooperative levels when sellers are given complete 
 cost and demand information, as compared with the case in which they must 
 learn about market demand and supply conditions through experience. 
 
 From an antitrust perspective, the standard approach to assessing the 
 likelihood of supra-competitive prices is to calculate measures of 
 
 Virginia Commonwealth University, University of Virginia and University 
 of Illinois, respectively. Financial assistance from the National Science 
 Foundation (SES 87-20105 and SES 89-09242) is gratefully acknowledged. 
 
 1 See the survey in Holt (1989). 
 
concentration, and then to consider factors that 'facilitate' collusion. 
 Rather than viewing these factors as unrelated, a careful antitrust analysis 
 should evaluate them collectively, in the context of the incentive structure 
 of the underlying market game. In particular, the concept of market power is 
 a useful way to organize the effects of qualitatively different 
 characteristics. Market power is generated when alteration of a particular 
 structural or institutional condition provides an incentive for one or more 
 firms to raise price above a common, competitive price level. 2 
 
 Since both the existence and recognition of market power may change witt 
 alterations in each of its underlying determinants, the purpose of this paper 
 is to provide a careful analysis of the relationship between pricing behavior 
 and market power, ceteris paribus. To do this, we designed a parallel series 
 of experiments, with without market power, where the trading institution, 
 excess supply, information conditions, and the number of sellers were held 
 constant. 3 
 
 Our primary focus is on market power in a static sense. This power 
 exists when one or more sellers can increase current profit with a unilateral 
 price increase above a common competitive level. It is not obvious, however, 
 
 2 A test for market power in this sense is based on the analysis of the 
 profitability of a unilateral price increase when initial prices are perfectly 
 competitive. This approach is basically motivated by the Department of Justice 
 Horizontal Merger Guidelines test. A firm (or group of firms) are said to have 
 market power if a small but significant price increase would be profitable. 
 
 3 Structural changes that can affect market power have been investigated 
 by others in laboratory markets. However, no research has isolated the effects 
 of market power on supra-competitive pricing, independent of the number of 
 sellers. This research differs from studies with explicit antitrust motivations, 
 e.g., Isaac and Reynolds (1989) and Wellford (1990). In such studies, a merger- 
 induced change in the number of sellers may have anticompetitive effects because 
 it creates market power, so it is natural to change both numbers and market 
 power. 
 
that static notions of market power are particularly relevant, because both 
 naturally occurring markets and laboratory markets evolve over time. In 
 repeated market periods, sellers must compare the long-term gains from 
 cooperating with the gains from a unilateral price reduction that may 
 instigate a price war. A relatively unprofitable equilibrium outcome in the 
 stage game can serve as a mutual punishment that is "triggered" by deviations 
 from higher, collusive prices. In other words, noncooperative equilibria in 
 the stage game can serve as punishments that support high levels of collusion 
 in dynamic, "trigger-price" equilibria. 4 
 
 Although noncooperative stage -game profits are typically higher in the 
 presence of static market power, the absence of this power may actually 
 increase market power in a dynamic sense. This is because the harsh penalty 
 of competitive pricing may enforce collusive outcomes more effectively than is 
 the case when static market power produces more profitable noncooperative 
 outcomes that serve as mutual punishments. If this observation is valid, the 
 antitrust implications are striking; markets that appear to be highly 
 competitive, e.g. markets with large excess capacity, many sellers, etc., may 
 in fact generate the least competitive price outcomes. With sufficiently low 
 discount rates, dynamic market power is pervasive, and this motivated our 
 decision to run parallel series of experiments, with and without static market 
 power, but always with enough dynamic power to support perfect collusion in a 
 trigger-price equilibrium. 
 
 Sections II and III below contain discussions of the experimental design 
 and procedures respectively. The price data is analyzed in section IV. The 
 
 4 These equilibria are analyzed in Friedman (1971) and Green and Porter 
 (1984), for example. 
 
results indicate that static market power has a clear, even dramatic, effect 
 in triopoly markets, but the effect in duopoly markets is less clear. The 
 final section contains a summary discussion. 
 
 II. Separating Market Power Predictions 
 
 Figure 1 presents the four market structures used in the experiments. 
 The market demand and supply functions in the four parts of this figure are 
 determined by buyers' values and sellers' costs [see Plott (1989) for a 
 discussion of standard procedures] . All values and costs are measured in 
 penny deviations from the perfectly competitive price, which is normalized to 
 zero. The experiments to be reported are posted-offer auctions, in which 
 sellers choose prices and maximum quantity amounts simultaneously, and buyers 
 may then purchase at the posted prices. In the analysis that follows, assume 
 that buyers are -passive price-takers who purchase all earnings -enhancing units 
 at the best available prices, and who divide their purchases equally between 
 sellers with equally low prices. 
 
 Consider first the 2-seller design with no market power, labeled 2SNP in 
 the upper left-hand part of figure 1. Sellers' units are indicated on the 
 market supply curve by seller designations, SI and S2, for sellers 1 and 2 
 respectively. Each seller has one unit with a cost of -35 and one unit with a 
 cost of 0. Two units are demanded inelastically at all prices less than or 
 equal to 60. The range of competitive prices is from -35 to 0. When demand 
 is divided equally at the maximum competitive price of 0, each seller sells 1 
 unit and earns profit of 35. Obviously, neither seller has static market 
 power at a common price of 0, since a unilateral price increase by either 
 would result in no sales and zero profits, and a price decrease would reduce 
 
earnings . 
 
 Market power can be introduced by increasing demand so that the high- 
 price seller in the range of supra -competitive prices will not lose all sales. 
 However, increasing demand in the 2SNP design reduces excess supply. As noted 
 above, low excess supply itself may have an upward influence on prices. 
 Therefore, we decided to increase demand and seller capacity together, in 
 order to maintain a constant level of excess supply. In our two -seller/power 
 design, labeled 2SP in figure 1, we doubled each seller's capacity and 
 increased demand to 6 units to maintain a constant excess capacity of 2 units. 
 When demand is divided equally at the (maximum) competitive price of zero, 
 each seller earns 70 on the sale of the two low-cost units. Static market 
 power exists in this design since a unilateral price increase now results in 
 the sale of the two low-cost units, but at a much higher earnings level. 
 
 The noncooperative equilibrium in the 2SP design involves randomization 
 over the range of prices that constitute an "Edgeworth cycle". 5 It is 
 straightforward to determine this randomization range when prices are real- 
 valued. The upper end of the Edgeworth cycle is a price of 60, where demand 
 exceeds either seller's capacity by 2 units, so either seller can earn a sure 
 profit of 2[60 - (-35)] - 190. However, the best response to one seller's 
 price of 60 is for the other to offer and sell 4 units at a price just below 
 60. Best responses to successively lower prices involve small price cuts, 
 until price falls to 30, since selling 4 units at a price below 30 is not as 
 profitable as selling 2 units at a price of 60. (Each seller always sells the 
 two low-cost units, so profit comparisons are equivalent to revenue 
 
 The equivalence of the Edgeworth cycle and the support of the mixed 
 distribution is valid in the present context, but not in general. See Holt and 
 Solis-Soberon (1990) for a counterexample. 
 
comparisons in this range, and 2 times 60 equals 4 times 30.) 
 
 Obviously, there is no pure -strategy equilibrium in this design, and 
 noncooperative sellers would attempt to price in an unpredictable manner in 
 order to avoid being slightly underpriced in the cycle. In equilibrium, 
 sellers must be indifferent over all prices in the support of the mixed 
 distribution, i.e. each price in this support must yield the security expected 
 profit of 190 that results from a price of 60. Formally, let G(p) denote the 
 probability that the price p posted by a seller i is the highest price posted 
 in the market for a period. Since sellers i and j have identical profit 
 functions, we will consider a symmetric mixed equilibrium in which G(p) is the 
 distribution function for the common price distribution. If a price p is the 
 highest price, the seller will sell 2 units, and will earn 
 
 H(p) - 2[p + 35] - 2p + 70. If p turns out to be the lowest price, the seller 
 sells two low-cost units and two high-cost units and earns 
 
 L(p) - 2[p + 35] + 2[p + 0] = 4p + 70. Recall that G(p) is the probability 
 that p is the higher price, so the expected profit is: 
 
 G(p)H(p) + [l-G(p) ]L(p) . Since a seller must be indifferent between all 
 prices over which randomization occurs, the function G(p) must equate the 
 expected profit at each price in [30,60] to the security profit at p = 60. 
 The resulting equation yields: 
 
 (1) G(p) - [4p - 120]/2p . 
 
 As can be verified, G(30) = 0, G(60) = 1, and G(40) = .5 . Therefore, the 
 median of the common mixed distribution is 40, and the expected profit is 190. 
 
 The analysis of the three-seller designs in figure 1 is analogous. In 
 the no-power design, 3SNP, each seller earns 35 on the sale of a single low- 
 
cost unit at the competitive price of 0. Each seller's capacity of 2 units 
 equals the excess supply at supra- competitive prices, so there is no market 
 power; a unilateral increase from a common competitive price will result in no 
 sales or profits. The 3-seller power design, 3SP, is obtained by doubling 
 each seller's capacity from 2 to 4 units and increasing demand from 4 to 10 
 units in order to maintain the 2 units of excess supply at prices in range 
 [0,60], The symmetric mixed distribution is calculated as before. First note 
 that each seller can be sure of selling 2 units at a price of 60, and the 
 security profit is 155 (profits of 95 on the single low-cost unit and 60 on 
 the high-cost unit) . If one of the triopolists posts a price p that turns out 
 to be the highest price, this seller would sell two units and earn 
 H(p) = 2p + 35. If the price is not the highest of the three prices, the 
 seller sells four units and earns L(p) = 4p + 35. Again let G(p) denote the 
 probability of having the highest price, so the expected profit is 
 G(p)H(p) + [1 - G(p)]L(p), which when equated to the security level of 155, 
 yields equation (1). Since G(30) = and G(60) = 1, sellers in the 3SP design 
 randomize in the range [30,60], as in the duopoly/power design. However, the 
 median price falls from 40 to 34. 6 
 
 The analysis of each of the 4 designs has been static, and the expected 
 profits from noncooperative behavior that have been derived are summarized in 
 the (N) row of Table 1. Now it is useful to consider the other extreme, 
 perfect collusion, which may be supported in each of the above designs by the 
 use of noncooperative stage-game equilibria as punishments for defection. In 
 
 6 Calculation of the median price in the triopoly is a bit more involved 
 than in the duopoly since G(p) , the probability that p is the highest price, is 
 now the probability that both of the other sellers price below p. If F(p) 
 denotes the common price distribution, G(p) - F(p) 2 , and therefore, F(p) = .5 
 when G(p) - .25, or when p is approximately 34. 
 
the 2SNP design, for example, if each seller picks the collusive price of 60 
 and limits quantity to 1, then they each earn 95. Now consider the incentive 
 for a seller to defect from this collusive arrangement. The defector could 
 sell 2 units at a price just below 60, for a profit of about 120 + 35 = 155. 
 The profits for collusion and defection in the other treatments are calculated 
 similarly, and are shown in the (C) and (D) rows of Table 1 respectively. For 
 each treatment, D > C > N. 
 
 In a trigger-price equilibrium, defection is followed by noncooperative 
 play forever. If x represents the constant probability of continuation to the 
 next period, the potential defector would earn D in the period of a defection 
 and would earn N in all subsequent periods, for an expected profit of 
 D + Nx/(l-x). This expected profit for defection (and punishment) is less 
 than the expected profit from collusion, C/(l-x) , if x > [D - C]/[D - N] . 
 This latter ratio, which will be called the Friedman coefficient, is 
 calculated in the bottom row of Table l. 7 By making the probability of 
 continuation exceed .5, it is possible to provide dynamic market power in all 
 designs. Moreover, the Friedman coefficient is the same for both paired 
 power/no -power designs. 
 
 III. Procedures 
 
 We conducted 4 experiments for each of the four designs, for a total of 
 16 posted-offer experiments. Half of these sessions (2 sessions in each of 
 the 4 treatment cells) were conducted at the University of Illinois (UI) , and 
 
 7 See Friedman (1971) 
 
used the PLATO implementation of the posted-offer institution. 8 The remaining 
 eight experiments were conducted at Virginia Commonwealth University (VCU) , 
 and used a networked-PC implementation of a posted-offer, written by Davis. 
 All participants in the VCU experiments were experienced in the sense that 
 they had previously participated in computerized posted-offer experiments, but 
 with different cohorts of subjects and experimental designs. 9 Participants in 
 the UI experiments were inexperienced. All seller participants were 
 undergraduate business students, who were paid a standard $3.00 appearance 
 fee, plus earnings from trades in the experiments. Buyers were simulated. 10 
 Sellers earned money by selling units at prices above their costs. Earnings 
 varied widely (between $7 and $55 per subject), but from all external 
 indications, subject motivation was excellent. 
 
 Identification codes for the 16 experiments listed in table 2 are 
 interpreted as follows: The number of sellers is indicated by 2S or 3S, the 
 presence or absence of static market power is indicated by P or NP , and 
 experience is indicated by an X. Finally, the last digit of each code is a 
 number 1-4, which distinguishes replications within treatment cells. Thus, 
 2SNP1 refers to the first experiment in the 2-seller/no-power treatment. 
 
 Sellers in a posted-offer auction choose prices and maximum sale 
 quantities simultaneously. After prices are displayed publicly, buyers are 
 selected in a random sequence and are given the opportunity to purchase at the 
 posted prices, up to the maximum sales quantities. For example, see Ketcham, 
 Smith and Williams (1984) for a description of the PLATO posted-offer program. 
 
 9 No VCU participant was in more than one of the experiments reported in 
 this paper. 
 
 10 Buyers are simulated because we are primarily interested in the 
 strategic behavior of sellers, when buyers have no countervailing power, e.g., 
 when there are many small buyers. In fact, buyers in posted-offer experiments 
 typically reveal demand fully [Ketcham, Smith and Williams (1984)]. However, 
 complete public information about costs and values may encourage strategic 
 withholding, especially with few buyers [Davis and Williams (1989)]. 
 
With the following notable exceptions, laboratory procedures were 
 standard for computerized posted-offer environments [see Ketcham, Smith, and 
 Williams (1984)]. First, although each participant proceeded though 
 interactive instructions presented at their own terminal, the instructions 
 were also read aloud by the experimenter. 11 Second, explicit information 
 regarding demand limit prices, as well as the purchasing decision of the 
 simulated buyers, was presented to participants, using an appropriate version 
 of the following message: 
 
 The buyers' side of the market in today's experiment is simulated. 
 There is a single buyer. This buyer will purchase units at 
 
 prices equal to or below $ , and will purchase no units at any 
 
 price above $ . If seller prices do not exceed $ , the 
 
 buyer will make purchases first from the seller posting the lowest 
 price, then from the seller with the second lowest price, and so* 
 forth. If two sellers post identical prices, then the buyer will 
 use the throw of a die to choose which seller to approach first. 
 Once a seller has been selected, the buyer will purchase all units 
 that can be afforded from that seller. If the buyer finishes 
 making purchases from one seller and still has more units 
 available, then the buyer will switch to the seller with the next 
 lowest price, and so forth. 
 
 This information was provided to more closely approximate the informational 
 assumptions underlying the static and dynamic game theories used to generate 
 the equilibrium power predictions. 12 13 Third, rather than stop each 
 
 11 Our experience in other contexts suggests that reading instructions 
 aloud facilitates learning, and it may also increase common knowledge regarding 
 procedures . 
 
 12 Participants were not explicitly told that all other sellers had 
 identical costs, although they may have assumed this. 
 
 13 The rationing procedure implemented in the simulated buyer 
 announcement, does not divide demand when prices are equal. Consequently, the 
 competitive equilibrium price of zero is not a noncooperative equilibrium 
 outcome, since each seller has an incentive to reduce price slightly to ensure 
 
 10 
 
experiment at a preset time for the entire session, or after a given number of 
 trading periods, we employed the following stopping rule: The experiment 
 proceeded uninterrupted for 15 periods. After period 15 and each subsequent 
 period, a 6-sided die was rolled, and the experiment was continued if the 
 outcome was 1-4 and stopped otherwise. Running uninterrupted for 15 periods 
 gave us a standard data set in all experiments. The 2/3 probability of 
 continuation was high enough to avoid end-period effects, i.e., it exceeds the 
 Friedman coefficients shown in table 1. Although subjects were recruited for 
 2 hours, experiments always ended at least 40 minutes early, and thus it was 
 extremely unlikely that the experiment would require more time than had been 
 scheduled on a single day. The stopping rule was publicly announced in 
 advance . 
 
 IV. Results 
 
 Before discussing specific results, we will discuss the way that the 
 data are presented. First, we report posted prices rather than contract 
 prices, because the static, mixed- strategy predictions derived in section II 
 pertain to posted prices. Second, we report the price medians rather than 
 means, since the median was calculated explicitly, and it places less weight 
 on a few very low and very high contract price postings in the inexperienced 
 
 the sale of the seller's low-cost unit. A mixed strategy equilibrium exists for 
 both the 2 and 3 person games, and each is very close to the competitive 
 equilibrium: The median for the 2SNP design is .5 cents, while the median price 
 for the 3SNP design is 2 cents. The mixing distributions are calculated exactly 
 as in the 2SP and 3SP designs, with security earnings equal to 35 (since either 
 seller can ensure a profit of approximately 35 by pricing slightly below 0. In 
 either design, each seller earns competitive profits (35) on average, and the 
 calculations in Table 1 are unaffected. Details are available on request. 
 
 11 
 
trials. 14 Finally, we pool the data from the experiments done at the two 
 locations (with different experience levels and computer PO implementations) , 
 since there is no statistically significant location effect. 15 
 
 Table 2 presents the medians of the posted prices for each of the 16 
 experiments for periods 11-15. When the four experiments in each of the four 
 treatment cells are pooled, the median prices for each period are plotted in 
 figure 2(a) for the 2SP and 2SNP treatments, and in figure 2(b) for the 3SP 
 and 3SNP treatments. In each figure, the competitive price is drawn as a 
 dotted extension from the relevant no-power design, illustrated on the left 
 side of the chart, while the lower and upper bounds of the static mixing 
 distribution (deviations of 30 and 60) are drawn as dotted extensions from the 
 relevant market power design, shown in the right side of the chart. Median 
 prices for the market-power design experiments are summarized in each figure 
 by a heavy bolded line, while median prices for the no-power design 
 experiments are summarized by the lighter line that connects a series of dots. 
 
 From examination of figure 2(b), it is clear that power dramatically 
 affects performance in the 3 -person experiments. The lower bound of the 
 mixing distribution cleanly separates median contract prices, with prices 
 approaching the limit price in the 3SP experiments and approaching a level of 
 10-15 cents over the competitive prediction in the 3SNP experiments. As 
 illustrated in figure 2(a), the median posted price path for the 2SP 
 
 14 Post-experiment comments by participants reveal that some of these 
 aberrant price postings were keystroke errors. 
 
 15 Using the median of prices across periods 11-15 for each experiment as 
 data points, a test of the null hypothesis of no experience effect generates a 
 t-test statistic of 0.62. A test of the same hypothesis using the unit 
 normalized version of the nonparametric Mann-Whitney test generates a test 
 statistic of 0.74. Neither statistic allows rejection of the null hypothesis 
 at conventional significance levels. 
 
 12 
 
experiments also lies above the median posted price path for the 2SNP 
 experiments. However, unlike the triopoly results, differences across power 
 treatments are small in the duopolies, and the lower bound of the mixing 
 distribution does not separate the power treatments nearly as well. 
 
 These data plots suggest several principal issues, which can be stated 
 as hypotheses about coefficients of a regression model. The dependent 
 variable will be the deviation of the median price from the competitive price, 
 denoted: P med - P e . Some cohorts of subjects are more competitive than others, 
 and therefore, prices in successive periods of a given experiment are unlikely 
 to be statistically independent. Consequently, we decided to use each of the 
 16 experiments to generate an independent observation, by calculating the 
 median of posted prices for periods 11-15 for each experiment. The two 
 independent variables are zero-one dummy variables: D_ = 1 when static market 
 power is present, and D 2 = 1 for the duopoly experiments. 
 
 The symmetric specification in equation (2) is convenient in that it 
 allows identification of static and dynamic market power effects in both the 
 two-person and three-person designs. 
 
 (2) P med - P e - [B 2 + B 2p D p ](D 2 ) + [B 3 + B 3p D p ](l-D 2 ) 
 
 The coefficients, B 2 and B 3 , are measures of tacit collusion in the 2 -seller 
 and 3-seller treatments respectively, while the coefficients B 2p and B 3 
 capture the incremental effects of introducing static market power. To see 
 this, suppose that there are two sellers (D 2 =1), so the right side of (2) 
 becomes: B 2 + B 2p D p . A positive and significant value of B 2 would indicate 
 that duopolists are able to collude tacitly to maintain prices above 
 
 13 
 
competitive levels, whether or not market power exists, and B 2p measures the 
 additional effect of introducing (static) market power in a duopoly. A 
 similar interpretation applies to B 3 and B 3p . 
 
 The primary null hypotheses to be considered are: 
 
 
 duopoly 
 
 
 
 triopolv 
 
 
 B 2 - 
 
 
 
 B 3 - 
 
 
 B 2P " 
 
 
 
 B 3p » 
 
 B 2 - 
 
 - 60, B 2p - 
 
 
 
 B 3 
 
 - 60, B 3p 
 
 no tacit collusion: 
 
 no market power effect: 
 
 perfect collusion: B 2 - 60, B 2p - B 3 = 60, B 3p - 0. 
 
 The perfect-collusion hypothesis is based on the exercise of dynamic market 
 power, since sellers are theoretically able to maintain collusive prices with 
 trigger-price strategies in all four treatments. 
 
 The OLS estimates of the parameters of equation (2) are: 
 
 (3) P med - P« » [23.6 + 7.87D p ](D 2 ) + [14.75 + 34. 75D p ] [1-D 2 ] 
 
 (3.69**) (0.875) (2.30*) (3.80**) 
 
 with R 2 =- .46, F (3 12) = 5.34*, and t-test statistics (for the null of no 
 difference from zero) printed below coefficient estimates. A single asterisk 
 by a test statistic indicates rejection of the null at a 95% confidence level, 
 while a double asterisk indicates rejection of the null at a 99% level 
 (direction not predicted) . These results provide statistical support for our 
 principle conclusions. 
 
 Market Power : First, the positive signs on the B 3p and B 2p coefficients 
 suggest that static market power generally increases prices. The large and 
 
 14 
 
statistically significant coefficient for the B 3p term indicates that static 
 market power effects are only important in the 3 -person markets, but the 
 coefficient for the B 2p is smaller and is not significant. The small marginal 
 effect of introducing market power in duopolies is probably due to the fact 
 that, with only two sellers, it is sometimes possible to maintain prices above 
 static noncooperative levels solely on the basis of mutual trust or implicit 
 threats (see the discussion of tacit collusion below) . 
 
 Conclusion 1: Static market power affects median prices , particularly in the 
 3 -person experiments. 
 
 Randomization : One obvious question is whether the supra-competitive pricing 
 in the power designs is due to randomization. In figure 2(a), median prices 
 are below the predicted level of 40 in the 2SP experiments. In figure 2(b), 
 median prices exceed the predicted level of 34 in the 3SP experiments, and 
 B 3p + B 3 - 49.5, which is far above the median price of the mixed distribution 
 for the stage game. Reexamination of median prices by experiment in table 2 
 provides further evidence of a lack of predicted randomization. For periods 
 11-15 of the 2SP and 3SP experiments, median prices are near the level 
 consistent with mixing in only one of the eight power design experiments 
 (experiment 2SPX4) . Aside from 2SPX4, prices in two of the remaining 2SP 
 design experiments are well below the 40 cent prediction (2SP1 and 2SPX3) and 
 (ignoring the posting error in 2SP2) are generally above it in 2SP2. In the 
 3SP design experiments, median prices exceed the 34 cent prediction consistent 
 with randomization in every period of every experiment by at least 7 cents. 16 
 
 16 Posted prices in Kruse , Rassenti, Reynolds, and Smith (1987) tended 
 toward the mean of the randomization distribution, although the hypothesis of 
 randomization could be rejected in most markets. Their design differed from the 
 
 15 
 
Thus, our second conclusion. 
 
 Conclusion 2: Although participants are able to maintain prices above 
 competitive levels in the market-power designs, they generally do not 
 randomize according to the static Nash predictions in these designs. 
 
 Tacit Collusion: The significance of the B 2 and B 3 coefficients indicates the 
 presence of tacit collusion, in the sense that prices are significantly 
 different from zero, independent of the effects of static market power. 
 Figures 2(a) and 2(b) provide additional evidence. In both no-power 
 treatments, median prices clearly exceed zero, even in the later periods: 
 Median deviations are on the order of 25 cents for periods 11-15 of the 2SNP 
 experiments, and 10 cents for periods 11-15 of the 3SNP experiments. Also, as 
 shown in figure 2(b), aggregate median prices for the last 5 periods of the 3- 
 seller/power experiments range between 45 and 50 cents, clearly above the 34 
 cent deviation consistent with randomization. Median prices in the 2SP 
 treatment, however, are on the order of 25-32 cents for the last 5 periods, 
 substantially below the 40 cent median in the static mixed equilibrium. 
 
 Examination of median posted prices by experiment provide some insight 
 into differences in the nature of the deviations. With the exception of the 
 3-seller/power cell, where median prices are almost uniformly near the 60 cent 
 limit price, there are particular instances where prices far exceed those 
 observed in the other experiments in the treatment cell (e.g. 2SNPX3, 3SNPX3, 
 and 2SP2, except for period 14). These occasional instances suggest the tacit 
 conspiratorial behavior that might generally be expected in thin markets. 
 
 design used in this paper, and sellers in their experiments were not given 
 complete demand information. We believe that the critical difference is the 
 difference in demand information, and we have been told by Kruse et al . that 
 higher prices are more prevalent in their subsequent (as yet unreported) 
 experiments with complete information. 
 
 16 
 
Also, the presence of high prices in 2SP2 suggests that there is nothing 
 particular about the 2SP design that hinders tacit conspiracy. Perhaps more 
 curious are the persistent deviations above both the competitive price and the 
 median price of the noncooperative equilibrium observed in the 3SP 
 experiments. However, with the exception of these 3SP experiments, there is 
 no evidence of perfect collusion resulting from the full exercise of dynamic 
 market power, which existed in all four designs. 
 
 Conclusion 3: Although participants infrequently adopt a profit maximizing 
 conspiracy, there is some evidence of tacit collusion in each of the treatment 
 cells, and median prices exceed the noncooperative prediction in 3 of the 4 
 cells . 
 
 Market Power and the Number of Sellers : An obvious question is why market 
 power has a more pronounced effect in the triopoly markets. The clean 
 separation of price performance across the power treatments in the triopoly 
 experiments illustrated in figure 2(b) also applies to the individual 
 experiments, as may be seen by again referring to table 2. In each of the 
 3SNP experiments, all median prices are at or below 30 (in fact 16 of the 20 
 prices are 15 cents or less) while median prices exceed 30 in each of the 
 experiments in the 3SP design. 
 
 In contrast, not only is the aggregate difference in prices across power 
 treatments smaller in the 2 -person experiments, but performance is much more 
 heterogenous. In the 2SNP experiments there are both nearly competitive price 
 postings (2SNPX4) and very high posted prices (2SNPX3) . Similarly, in the 2SP 
 experiments, there are both low median prices (2SP1) and high median prices 
 (2SP2 and 2SPX4) . It appears that, independent of static market power 
 conditions in duopolies, sellers are occasionally able to tacitly conspire, 
 and also occasionally price very competitively. Cooperative opportunities may 
 
 17 
 
increase with decreases in the number of sellers for standard reasons, e.g., 
 with only two sellers it is easy to punish cheating directly. In addition, 
 increased rivalry may be a consequence of providing demand information. If 
 the sellers assume cost symmetry, they may start to view relative earnings as 
 more important than total earnings. 17 We summarize this discussion as a 
 conjecture: 
 
 Conjecture: The capacity to both directly monitor and punish competitors in 
 full information duopolies provides increased opportunities for tacit 
 conspiracy, and increased rivalry; and therefore generates much more variable 
 pricing performance. 
 
 V. Conclusion 
 
 Seller market power exists in a static sense when one or more sellers 
 can profit from a unilateral increase in price above the competitive level 
 (and consequently the competitive price is not a noncooperative equilibrium in 
 the stage game). In laboratory experiments ,* a small number of sellers with 
 market power are sometimes able to exercise it, especially in posted-offer 
 markets. In the duopoly and triopoly posted-offer experiments reported here, 
 market power is induced by having a relatively small (two -unit) excess supply 
 at supra-competitive prices, to ensure that price increases do not result in 
 large quantity reductions. An important question is whether the observed 
 supra-competitive pricing is a result of market power as a theoretical 
 construct, or whether it is an artifact of either small numbers or of small 
 excess supply above the competitive price. This question is addressed by 
 running control experiments in which market power is eliminated by 
 simultaneously reducing demand and giving each seller a lower capacity that 
 
 17 See, Holt (1989) for an expanded discussion of these effects 
 
 18 
 
just equals excess supply at supra-competitive prices. Although there is no 
 static market power in the control, the probabilistic termination rule admits 
 the possibility of "collusive" outcomes, supported by trigger price 
 strategies, in both the power and no-power designs. 
 
 In the no-power treatments, observed posted prices significantly 
 exceeded static noncooperative levels, which indicates some degree of tacit 
 collusion in both the duopoly and triopoly markets. However, this supra- 
 competitive pricing cannot be explained by the full exercise of dynamic market 
 power, since prices were never close to the perfectly collusive level. The 
 introduction of static market power is associated with higher posted prices, 
 especially with three sellers. The observed prices in triopoly markets with 
 power are even higher than the levels predicted by the static noncooperative 
 equilibrium exercise of market power, which again indicates some degree of 
 tacit collusion in these repeated market games. 
 
 The results in the duopoly markets are more variable; some duopolies 
 generate high prices and others exhibit more rivalistic behavior. 18 One would 
 expect more disperse results with fewer participants, since individual 
 differences have a larger effect in small markets. In addition, incentive 
 effects may induce variability in 2-seller pricing decisions. With a single 
 rival, it is possible to direct a punishment at that rival without sending a 
 message to a third person, which may facilitate tacit collusion. On the other 
 hand, duopolists may be more likely to become envious and vindictive, which 
 may cause some duopolies to end up being very competitive. These opposing 
 tendencies could produce varied results across duopoly experiments. 
 
 18 Similarly, Dolbear et al . (1968) reported more variability in markets 
 with 2 sellers than with 4 sellers. 
 
 19 
 
REFERENCES 
 Davis, Douglas D. and Charles Holt, "List Prices and Discounts," draft, 
 
 University of Virginia, October 1989. 
 Davis, Douglas D. and Arlington Williams, "The Effects of Market Information 
 
 on Pure Bargaining Equilibria in Laboratory Markets," draft, Virginia 
 
 Commonwealth University, March 1989. 
 Davis, Douglas D. and Arlington Williams, "On the Hayek Hypothesis in 
 
 Experimental Auctions: Institutional Effects and Market Power," 
 
 forthcoming in Economic Inquiry . 
 Dolbear, F.T. et al . . "Collusion in Oligopoly: An Experiment on the Effect of 
 
 Numbers and Information," Quarterly Journal of Economics . 82, May 1968, 
 
 240-59. 
 Friedman, James, "A Noncooperative Equilibrium for Supergames," Review of 
 
 Economic Studies . 38, 1971, 1-12. 
 Green, Edward, and Robert Porter, "Noncooperative Collusion Under Imperfect 
 
 Price Information," Econometrica . 52, 1984, 87-100. 
 Holt, Charles A., "The Exercise of Market Power in Laboratory Experiments," 
 
 Journal of Law and Economics . October 1989, 32, S107-S130. 
 Holt, Charles A. , and Fernando Solis-Soberon, "The Calculation of Mixed- 
 Strategy Equilibria in Posted-Offer Markets," University of Virginia, 
 
 Thomas Jefferson Center for Political Economy working paper, January 
 
 1990. 
 Holt, Charles A., Loren W. Langan, and Anne P. Villamil, "Market Power in Oral 
 
 Double Auctions," Economic Inquiry . 24, 1986, 107-123. 
 Hong, James T. and Charles R. Plott, "Rate Filing Policies for Inland 
 
 Transportation, An Experimental Approach," Bell Journal of Economics . 
 
 20 
 
13, Spring 1982, 1-19. 
 
 Isaac, Mark, and Stanley Reynolds, "Two or Four Firms: Does It Matter?" draft, 
 
 University of Arizona, June 1989. 
 Ketcham, J., Vernon L. Smith, and Arlington Williams, "A Comparison of Posted- 
 
 Offer and Double -Auction Pricing Institutions," Review of Economic 
 
 Studies . 51, 1984, 595-614. 
 Kruse, Jamie, Steven Rassenti, Stanley S. Reynolds, and Vernon L. Smith, 
 
 "Bertrand-Edgeworth Competition in Experimental Markets," working paper, 
 
 University of Arizona, November 1987. 
 Plott, Charles R. , "An Updated Review of Industrial Organization: Applications 
 
 of Experimental Methods," in Handbook of Industrial Organization, Volume 
 
 II . (R. Schmalensee and R.D. Willig, eds . ) , Elsevier Science Publishers: 
 
 New York, 1989. 
 Plott, Charles R. and Vernon L. Smith, "An Experimental Examination of Two 
 
 Exchange Institutions," Review of Economic Studies . 45, 1978, 133-153. 
 Smith, Vernon L. , "Experimental Auction Markets and the Walrasian Hypothesis," 
 
 Journal of Political Economy . 73, August 1965, 387-93. 
 Wellford, Charissa, "Horizontal Mergers: Policy and Performance," draft, 
 
 University of Arizona, 1989. 
 
 21 
 
Table 1. Calculation of Profits and the Friedman Coefficient, by Treatment 
 
 seller/power treatment: 2SNP 2SP 3SNP 3SP 
 
 noncooperative profits (N) : 35 190 35 155 
 
 collusive profits (C) : 95 250 115 235 
 
 unilateral defection profits (D) : 155 310 155 275 
 
 Friedman coefficient [D - C]/[D - N] : .5 .5 .33 .33 
 
 22 
 
Table 2. Median Posted Prices for Periods 11-15 
 
 2 Sellers, No Power 
 Period 2SNP1 2SNP2 2SNPX3 2SNPX4 
 
 2 Sellers, Power 
 2SP1 2SP2 2SPX3 
 
 2SPX4 
 
 11 
 
 19 
 
 22 
 
 26 
 
 -1 
 
 17 
 
 52 
 
 35 
 
 40 
 
 12 
 
 28 
 
 22 
 
 40 
 
 3 
 
 13 
 
 42 
 
 34 
 
 50 
 
 13 
 
 25 
 
 26 
 
 53 
 
 5 
 
 13 
 
 29 
 
 38 
 
 40 
 
 14 
 
 23 
 
 23 
 
 49 
 
 23 
 
 18 
 
 -11* 
 
 29 
 
 30 
 
 15 
 
 20 
 
 15 
 
 49 
 
 8 
 
 21 
 
 60 
 
 21 
 
 21 
 
 3 Sellers, No Power 3 Sellers, Power 
 
 Period 3SNP1 3SNP2 3SNPX3 3SNPX4 3SP1 3SP2 3SPX3 3SPX4 
 
 11 
 
 2 
 
 20 
 
 15 
 
 15 
 
 57 
 
 47 
 
 51 
 
 35 
 
 12 
 
 2 
 
 15 
 
 15 
 
 15 
 
 63 
 
 45 
 
 53 
 
 60 
 
 13 
 
 2 
 
 13 
 
 30 
 
 14 
 
 59 
 
 45 
 
 52 
 
 48 
 
 14 
 
 2 
 
 11 
 
 30 
 
 15 
 
 59 
 
 44 
 
 53 
 
 41 
 
 15 
 
 2 
 
 9 
 
 30 
 
 10 
 
 55 
 
 43 
 
 54 
 
 60 
 
 * One participant commented that he mistakenly entered a price that was $1.00 
 below his intended price in this period. The median price for this period 
 would have been 60 had the participant entered his intended price. 
 
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