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43
Quantal Response Equilibria For Normal Form Games
 NORMAL FORM GAMES, GAMES AND ECONOMIC BEHAVIOR
, 1995
"... We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish e ..."
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Cited by 392 (22 self)
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We investigate the use of standard statistical models for quantal choice in a game theoretic setting. Players choose strategies based on relative expected utility, and assume other players do so as well. We define a Quantal Response Equilibrium (QRE) as a fixed point of this process, and establish existence. For a logit specification of the error structure, we show that as the error goes to zero, QRE approaches a subset of Nash equilibria and also implies a unique selection from the set of Nash equilibria in generic games. We fit the model to a variety of experimental data sets by using maximum likelihood estimatation.
An Experimental Study of Belief Learning Using Elicited Beliefs
 Econometrica
, 2000
"... This paper investigates belief learning. Unlike other investigators who have been forced to use observable proxies to approximate unobserved beliefs, we have, using a belief elicitation procedure (proper scoring rule), elicited subject beliefs directly. As a result we were able to perform a more dir ..."
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Cited by 62 (1 self)
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This paper investigates belief learning. Unlike other investigators who have been forced to use observable proxies to approximate unobserved beliefs, we have, using a belief elicitation procedure (proper scoring rule), elicited subject beliefs directly. As a result we were able to perform a more direct test of the proposition that people behave in a manner consistent with belief learning. What we find is interesting. First...
LABORATORY EXPERIMENTATION IN ECONOMICS: A METHODOLOCICAL OVERVIEW
, 1988
"... Informal experimentation in economics goes back at least as far as Bernoulli (1738) (in connection with the Petersburg game), and formal reports of laboratory experiments as such have appeared for some time now (see e.g. ..."
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Cited by 21 (0 self)
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Informal experimentation in economics goes back at least as far as Bernoulli (1738) (in connection with the Petersburg game), and formal reports of laboratory experiments as such have appeared for some time now (see e.g.
Buyer search and price dispersion: a laboratory study
, 2003
"... We study markets with costly buyer search in which sellers simultaneously post prices. Buyers costlessly observe one or (with probability 1 q) two of the posted prices, and can accept one or pay to search again. The experiment varies q, the search cost, and the number of buyers. Equilibrium theory p ..."
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Cited by 20 (4 self)
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We study markets with costly buyer search in which sellers simultaneously post prices. Buyers costlessly observe one or (with probability 1 q) two of the posted prices, and can accept one or pay to search again. The experiment varies q, the search cost, and the number of buyers. Equilibrium theory predicts a unified very low (high) price for q=0 (q=1) and predicts specific distributions of dispersed prices for q=1/3 and 2/3. Actual prices conform closely to the predictions in some treatments. Buyers’ reservation prices are biased away from the extremes, however, and sellers’ prices have positive autocorrelation and crosssectional correlation.
Mixed Strategy Play and the Minimax Hypothesis
 JOURNAL OF ECONOMIC THEORY
, 1996
"... This paper reports on a set of experiments designed to discriminate among the possible sources of the failure of the unique mixed strategy minimax equilibrium of the O'Neill (1987) game. First, the experimental design allows one to identify the causes of the serial correlation in subjects' action ..."
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Cited by 20 (3 self)
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This paper reports on a set of experiments designed to discriminate among the possible sources of the failure of the unique mixed strategy minimax equilibrium of the O'Neill (1987) game. First, the experimental design allows one to identify the causes of the serial correlation in subjects' action choices. Second, the design allows one to discriminate among a set of mixed strategies which generate distributions over actions and wins similar to the distributions generated by the minimax strategy. This is accomplished by introducing a new methodology for eliciting mixed strategies, which overcomes some of the difficulties with previous experimental attempts to directly observe mixed strategies. The results clearly show that subjects' choices do not coincide with their minimax strategies, and that players' intended behavior is not minimax. Analysis of the data also reveals that subjects adopt a wide variety of strategies. It is shown that this heterogeneity can rationalize some ...
The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence
, 2009
"... A usual criticism of the theory of infinitely repeated games is that it does not provide sharp predictions since there may be a multiplicity of equilibria. To address this issue we present experimental evidence on the evolution of cooperation in infinitely repeated prisoners ’ dilemma games as subje ..."
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Cited by 17 (1 self)
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A usual criticism of the theory of infinitely repeated games is that it does not provide sharp predictions since there may be a multiplicity of equilibria. To address this issue we present experimental evidence on the evolution of cooperation in infinitely repeated prisoners ’ dilemma games as subjects gain experience. We find that cooperation decreases with experience when it cannot be supported as an equilibrium outcome. More interestingly, the converse is not necessarily true: cooperation does not always increase with experience when it can be supported as an equilibrium outcome. Nor is a more stringent condition, risk dominance, sufficient for cooperation to arise. However, subjects do learn to cooperate when the payoff to cooperation and the importance of the future is high enough. These results have important implications for the theory of infinitely repeated games. While we show that cooperation may prevail in infinitely repeated games, the conditions under which this occurs are more stringent than the subgame
Professionals Play Minimax
 REVIEW OF ECONOMIC STUDIES
, 2003
"... The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a oneshot twoperson zerosum game. The results of the tests are remarkably consistent with equilibrium play i ..."
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Cited by 14 (1 self)
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The implications of the Minimax theorem are tested using natural data. The tests use a unique data set from penalty kicks in professional soccer games. In this natural setting experts play a oneshot twoperson zerosum game. The results of the tests are remarkably consistent with equilibrium play in every respect: (i) winning probabilities are statistically identical across strategies for players; (ii) players’ choices are serially independent. The tests have substantial power to distinguish equilibrium play from disequilibrium alternatives. These results represent the first time that both implications of von Neumann’s Minimax theorem are supported under natural conditions.
Experientia Docet: Professionals Play Minimax in Laboratory Experiments
 Econometrica
, 2008
"... We study how professional players and college students play zerosum twoperson strategic games in a laboratory setting. We first ask professionals to play a 2x2 game that is formally identical to a strategic interaction situation that they face in their natural environment. We find that these subjec ..."
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Cited by 11 (0 self)
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We study how professional players and college students play zerosum twoperson strategic games in a laboratory setting. We first ask professionals to play a 2x2 game that is formally identical to a strategic interaction situation that they face in their natural environment. We find that these subjects play in the laboratory exactly as in the field, that is as the equilibrium of the game dictates: (i) they equate payoffs across strategies, and (ii) generate sequences of choices that are random. In sharp contrast with them, however, we also find that college students play the game far from the equilibrium predictions. We then study the behavior of professional players and college students in the classic O’Neill’s 4x4 zerosum game, a game that none of the subjects have encountered previously, and find the same drastic differences in behavior between these two subject pools. The transfer of skills and experience from the familiar field to the unfamiliar laboratory observed for professional players is relevant, from a methodological perspective, to evaluate the circumstances under which behavior in a laboratory setting may be a reliable indicator of behavior in a naturally occurring setting. From a cognitive perspective, it is useful for research on recognition processes, intuition, and similarity as a basis for inductive reasoning.
Market Power and Mergers in Laboratory Markets with Posted Prices
"... This paper uses laboratory methods to evaluate determinants of supracompetitive pricing. The experiment involves three treatments, each with the same market supply, demand, and competitive price. In the baseline treatment, capacity is divided among five sellers so that the competitive price is a Na ..."
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Cited by 11 (0 self)
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This paper uses laboratory methods to evaluate determinants of supracompetitive pricing. The experiment involves three treatments, each with the same market supply, demand, and competitive price. In the baseline treatment, capacity is divided among five sellers so that the competitive price is a Nash equilibrium. Market power is created in a second treatment by reallocating capacity among the sellers. This market power raises observed prices in all sessions. In a third treatment, the three smallest sellers are merged in a way that holds market power constant. The consolidation has little residual effect on prices.
An Experimental Investigation of Unprofitable Games
, 2002
"... We investigate behavior in two unprofitable games—where Maxmin strategies do not form a Nash equilibrium yet guarantee the same payoff as Nash equilibrium strategies—that vary in the riskiness of the Nash strategy. We find that arguments for the implausibility of Nash equilibrium are confirmed by ou ..."
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Cited by 10 (0 self)
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We investigate behavior in two unprofitable games—where Maxmin strategies do not form a Nash equilibrium yet guarantee the same payoff as Nash equilibrium strategies—that vary in the riskiness of the Nash strategy. We find that arguments for the implausibility of Nash equilibrium are confirmed by our experiments; however, claims that this will lead to Maxmin play are not. Neither solution concept accounts for more than 53 % of choices in either game. The results indicate that the tension between the Nash and Maxmin strategies does not resolve itself over the course of the experiment. Moreover, the relative performance of the solution concepts is sensitive to the riskiness of the Nash strategy.