Y2K Bibliography of Experimental Economics and Social Science
Matrix Games

Charles A. Holt, cah2k@virginia.edu, suggestions and corrections welcome
(for online and personal use only)


Abbink, Klaus, Joachim Buchta, Abdolkarim Sadrieh, and Reinhard Selten (1998) “How to Play 3x3-Games,” University of Bonn, Discussion Paper, presented at the Summer 1998 ESA Meeting. Keywords: experiments, game theory, matrix games. Abstract: Subjects submitted strategies for playing 3x3 matrix games, which were translated into computer programs. The programs were randomly matched in a computer tournament. Behavior converged toward the predictions of a pure-strategy equilibrium. Email Contact: selten@lab.econ1.uni-bonn.de, abbink@lab.econ1.uni-bonn.de

Anderson, Simon P., Jacob Goeree, and Charles A. Holt (1998) “Control Costs and Equilibria in Games with Bounded Rationality,” University of Virginia, Discussion Paper, presented at the Summer 1998 ESA Meeting. Keywords: experiments, game theory, control costs, quantal response equilibrium. Abstract: Van Damme's notion of control costs is that it is more costly to implement decisions more precisely. This paper derives the relationship between control costs and noisy approaches to equilibrium in games. In two-by-two games, quantal response equilibria are equivalent to Nash equilibria with control costs. Extensions to N-person matrix games are also discussed. Email Contact: jg2n@virginia.edu

Bouchez, Nichole Marie (1999) “Learning Models in a Three by Three Bimatrix World,” University of California at Santa Cruz, Discussion Paper, presented at the Summer 1999 ESA Meeting. Keywords: experiments, game theory, learning, 3x3 matrix games, belief learning, reinforcement learning. Email Contact: bouchez@cats.ucsc.edu

Brandts, Jordi, and Charles A. Holt (1992) “Forward Induction: Experimental Evidence from Two-stage Games with Complete Information,” in Research in Experimental Economics, Vol. 5, edited by R. M. Isaac, Greenwich, Conn.: JAI Press, 119-136. Keywords: experiments, game theory, forward induction, matrix games, two-stage games. Abstract Forward induction formalizes the idea that actions taken in an early stage of a game can restrict reasonable beliefs about play off of the equilibrium path, which in turn can rule out equilibria that satisfy backward induction rationality. Observed play tends to converge to the equilibrium that is not ruled out by forward induction arguments. Email Contact: brandts@cc.uab.es

Brown, J. N., and Robert W. Rosenthal (1990) “Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment,” Econometrica, 58:5 (September), 1065-1081. Keywords: experiments, game theory, mixed strategies, matrix games.

Chen, Hsiao-Chi, James W. Friedman, and Jacques-Francois Thisse (1996) “Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach,” Games and Economic Behavior, 1832-54. Keywords: experiments, game theory, matrix games, quantal response, bounded rationality, learning. Abstract: This paper uses the Luce probabilistic choice rule to analyze behavior in matrix games.

Cooper, Russell, Douglas V. DeJong, Robert Forsythe, and Thomas W. Ross (1989) “Communication in the Battle of the Sexes Game: Some Experimental Results,” Rand Journal of Economics, 20:4 (Winter), 568-587. Keywords: experiments, game theory, battle of sexes game, coordination, matrix games, communication. Email Contact: rcooper@bu.edu

Cooper, Russell, Douglas V. DeJong, Robert Forsythe, and Thomas W. Ross (1990) “Selection Criteria in Coordination Games: Some Experimental Results,” American Economic Review, 80:1 (March), 218-233. Keywords: experiments, game theory, matrix games, coordination games, equilibrium selection. Email Contact: rcooper@bu.edu

Cooper, Russell, Douglas V. DeJong, Robert Forsythe, and Thomas W. Ross (1992) “Communication in Coordination Games,” Quarterly Journal of Economics, 107:2 (May), 739-771. Keywords: experiments, game theory, matrix games, coordination game, communication. Email Contact: rcooper@bu.edu

Davis, Douglas D., and Charles A. Holt (1999) “Equilibrium Cooperation in Two-Stage Games: Experimental Evidence,” International Journal of Game Theory, 28:1 (February), 89-109. Keywords: experiments, game theory, cooperation, matrix games, two-stage games, renegotiation proofness, backward induction, punishments. Abstract: Subjects play two-stage matrix games in which cooperation in the first stage can be supported by punishments and rewards in a second-stage game that has a battle-of-sexes structure. Some cooperation is supported in this manner, even when the punishment outcome is not a Nash equilibrium. The data are inconsistent with the notion of renegotiation proofness. Email Contact: ddavis@busnet.bus.vcu.edu

Duffy, John, and Nick Feltovich (1999) “Words, Deeds, and Lies,” University of Houston, Discussion Paper, presented at the Fall 1999 European Regional ESA Meeting. Keywords: experiments, game theory, coordination, matrix games, cheap talk, reputations. Abstract: Subjects are randomly matched in 2x2 coordination games, and the subject designated as a "sender" sends a message about intended play, which is read by the "receiver" prior to the point at which both make their decisions. Messages are more effective in the treatment where the receiver also sees that sender's message/action decisions from the most recent matching, as compared with a baseline treatment where only the sender's previous action is revealed. Email Contact: nfelt@bayou.uh.edu

Goeree, Jacob K., and Charles A. Holt (1999) “A Model of Noisy Introspection,” University of Virginia, Discussion Paper. Keywords: experiments, game theory, introspection, logit equilibrium. Abstract: The paper presents a theoretical model of noisy iterated introspection designed to explain behavior in games played only once. The model determines layers of beliefs (about others' decisions, others' beliefs, beliefs about beliefs...), but relaxes the Nash-like requirement that belief distributions coincide with distributions of decisions, i.e. it allows for systematic surprises in the absence of learning and repetition. The introspective solution exists and nests standard Nash and quantal response equilibrium theories, which are rejected on the basis of maximum likelihood estimates of noise and introspection parameters for laboratory data from thirty-seven variations of 2x2 games played once. Email Contact: jg2n@virginia.edu

Huck, Steffen, Hans-Theo Normann, and Jörg Oechssler (2000) “Does Information About Competitors' Actions Increase or Decrease Competition in Experimental Oligopoly Markets?,” International Journal of Industrial Organization, 18:1 (January), 39-57. Keywords: experiments, markets, matrix games, strategic substitutes and complements, information effects. Abstract: Evidence from Bertrand and Cournot type experiments indicates that more information about others' actions does not promote tacit collusion. There is some tendency for subjects with good information to imitate actions that earned high payoffs, which tends to make the outcomes more competitive. Email Contact: normann@wiwi.hu-berlin.de, oechssler@uni-bonn.de

Knapp, Robert, and Andreas Ortmann (1998) “On the Use of Evolutionary Models in Experimental Economics,” Bowdoin College, Keywords: experiments, game theory, evolution, replicator dynamics, learning, matrix game. Abstract: Data from a bargaining experiment in matrix form are used to evaluate a variety of evolutionary models. There is no clear winner.

Lieberman, Bernhardt (1960) “Human Behavior in a Strictly Determined 3x3 Matrix Game,” Behavioral Science, 4317-322. Keywords: experiments, game theory, matrix game.

Lieberman, Bernhardt (1962) “Experimental Studies of Conflict in Some Two-Person and Three-Person Games,” in Mathematical Models in Small Group Processes, edited by J. H. Criswell, H. Solomon and P. Suppes, Stanford: Stanford University Press, 203-220. Keywords: experiments, game theory, matrix game. Email

McKelvey, Richard D., Thomas R. Palfrey, and Roberto Weber (1997) “The Effects of Payoff Magnitude and Heterogeneity on Behavior in 2x2 Games with Unique Mixed Strategy Equilibria,” California Institute of Technology, working paper. Keywords: experiments, game theory, mixed strategies, quantal response equilibrium, logit equilibrium, payoffs, incentives. Email Contact: rdm@hss.caltech.edu

Morgan, John, and Martin Sefton (1998) “An Experimental Investigation of Unprofitable Games,” Princeton University, Discussion Paper, presented at the Fall 1998 ESA Meetings. Keywords: experiments, game theory, matrix games, maxmin behavior, Nash equilibrium, quantal response equilibrium. Abstract: An unprofitable game is one in which maximin strategies do not constitute a Nash equilibrium, yet they guarantee the same payoff as players earn in a Nash equilibrium. In two-person matrix games with three strategies, the data patterns do not correspond to either Nash or maximin play. Email Contact: jmorgan@princeton.edu, martin.sefton@newcastle.ac.uk

My, K. Boun, Marc Willinger, and A. Ziegelmeyer (1998) “Local Interaction and Equilibrium Selection: An Experimental Investigation,” BETA, Discussion Paper, presented at the Summer 1998 ESA Meeting. Keywords: experiments, game theory, local interaction, equilibrium selection. Abstract: This experiment evaluates the effects of local versus global interaction on behavior in two-person 2x2 coordination games. Other treatment variables include the size of the local neighborhoods. Email Contact: willma@cournot.u-strasbg.fr

O'Neil, Barry (1987) “**Nonmetric Test of the Minimax Theory of Two-Person Zerosum Games,” Proceedings of the National Academy of Sciences, 842106-2109. Keywords: experiments, game theory, mixed strategy play, minimax theorem, matrix game.

Rapoport, Anatol (1959) “Critiques of Game Theory,” Behavioral Science, 449-66. Keywords: experiments, game theory, matrix games, survey.

Rapoport, Amnon, and David V. Budescu (1992) “Generation of Random Series in Two-Person Strictly Competitive Games,” Journal of Experimental Psychology: General, 121352-363. Keywords: experiments, game theory, mixed strategies, matrix games. Email Contact: arapoport@bpa.arizona.edu

Rapoport, Anatol, Oded Frenkel, and Josef Perner (1977) “Experiments with Cooperative 2X2 Games,” Theory and Decision, 867-92. Keywords: experiments, game theory, 2x2 games.

Rapoport, Anatol, Melvin J. Guyer, and David G. Gordon (1976) The 2x2 Game, Ann Arbor: University of Michigan Press. Keywords: experiments, game theory, matrix games.

Rapoport, Anatol, and Carol Orwant (1962) “Experimental Games: A Review,” Behavioral Science, 71-37. Keywords: experiments, game theory, matrix games, survey.

Shubik, Martin (1996) “Why Equilibrium? A Note on the Noncooperative Equilibria of Some Matrix Games,” Journal of Economic Behavior and Organization, 29:3 (May), 537-539. Keywords: experiments, game theory, Nash equilibrium, matrix games. Email Contact: martin.shubik@yale.edu

Stahl, David O. (1988) “On the Instability of Mixed Strategy Nash Equilibria,” Journal of Economic Behavior and Organization, 9:1 (January), 59-69. Keywords: experiments**, game theory, mixed strategies, stability, matrix games. Email Contact: stahl@eco.utexas.edu