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Learning to be imperfect: The ultimatum game. (English) Zbl 0827.90146

Summary: This paper studies interactive learning processes that are subject to constant perturbations or “noise”. We argue that payoffs in the ultimatum game are such that responders are more apt to be “noisy” than are proposers and show that as a result the learning process readily leads to outcomes that are Nash equilibria but not subgame-perfect. We conclude that game theorists should not restrict attention to the subgame-perfect equilibrium when predicting laboratory behavior in the ultimatum game.

MSC:

91A26 Rationality and learning in game theory
91A90 Experimental studies
91E40 Memory and learning in psychology
Full Text: DOI

References:

[1] Andreoni, J.; Miller, J. H., Auctions with aritificial adaptive agents (1993), University of Wisconsin, Carnegie Mellon University, Pittsburgh, PA
[2] Bendor, J.; Mookherjee, D.; Ray, D., Aspiration-based adaptive learning in two person repeated games (1991), Indian Statistical Institute: Indian Statistical Institute Madison, WI, mimeo
[3] Binmore, K., Modeling Rational Players: I and II, Economics and Philosophy, 4, 9-55 (1987/1988)
[4] Binmore, K., Essays on the Foundations of Game Theory (1990), Basil Blackwell: Basil Blackwell Cambridge, MA · Zbl 0774.90093
[5] Binmore, K., Fun and Games (1992), Heath: Heath Lexington, MA · Zbl 0757.90087
[6] Binmore, K.; Samuelson, L., Muddling through: Noisy equilibrium selection (1993), University College London; University of Wisconsin, mimeo · Zbl 0887.90191
[7] Binmore, K.; Samuelson, L., An Economist’s Perspective on the Evolution of Norms, J. Institutional Theoretical Economics, 150, 45-63 (1994)
[8] Binmore, K.; Samuelson, L.; Vaughan, R., Musical chairs: Modelling noisy evolution (1993), University College London; University of Wisconsin, mimeo
[9] Binmore, K.; Shaked, A.; Sutton, J., An Outside Option Experiment, Quart. J. Econ., 104, 753-770 (1989)
[10] Binmore, K.; Swierzbinski, J.; Hsu, S.; Proulx, C., Focal points and Bargaining, (Discussion Paper (1992), University of Michigan) · Zbl 0784.90109
[11] Bolton, G. E., A Comparative Model of Bargaining: Theory and Evidence, Amer. Econ. Rev., 81, 1096-1136 (1991)
[12] Bolton, G. E.; Zwick, R., Anonymity versus punishment in ultimatum bargaining (1993), Pennsylvania State University, mimeo · Zbl 0831.90137
[13] Börgers, T.; Sarin, R., Learning through reinforcement and replicator dynamics, (technical report (1993), University College London) · Zbl 0892.90198
[14] Cabrales, A., Stochastic replicator dynamics (1993), University of California, mimeo
[15] Crawford, V. P., An ‘Evolutionary’ Interpretation of Van Huyck, Battalio, and Beil’s Experimental Results on Coordination, Games Econ. Behav., 3, 25-59 (1991) · Zbl 0825.90836
[16] Crawford, V. P., Adaptive dynamics in coordination games, (Department of Economics Working Paper 92-02R (1992), University of California: University of California San Diego) · Zbl 0827.90143
[17] Frank, R., Passions within Reason (1988), Norton: Norton New York
[18] Guth, W.; Schmittberger, R.; Schwarze, B., An Experimental Analysis of Ultimatum Bargaining, J. Econ. Behav. Organ., 3, 367-388 (1982)
[19] Güth, W.; Tietz, R., Ultimatum Bargaining Behavior: A Survey and Comparison of Experimental Results, J. Econ. Psychol., 11, 417-449 (1990)
[20] Hofbauer, J.; Sigmund, K., The Theory of Evolution and Dynamical Systems (1988), Cambridge Univ: Cambridge Univ Cambridge · Zbl 0678.92010
[21] Kahneman, D.; Tversky, A., Rational Choice and the Framing of Decisions, (Decision Making (1988), Cambridge Univ.: Cambridge Univ. Cambridge) · Zbl 1225.91017
[22] Kandori, M.; Mailath, G. J.; Rob, R., Learning, Mutation, and Long Run Equilibria in Games, Econometrica, 61, 29-56 (1993) · Zbl 0776.90095
[23] Kohlberg, E.; Mertens, J.-F., On the Strategic Stability of Equilibria, Econometrica, 54, 1003-1038 (1986) · Zbl 0616.90103
[24] Ledyard, J., Public goods: A survey of experimental research, (working paper (1992), California Institute of Technology)
[25] Miller, J. H.; Andreoni, J., Can Evolutionary Dynamics Explain Free Riding in Experiments?, Econ. Lett., 36, 9-15 (1991) · Zbl 0729.90627
[26] Myerson, R. B., Game Theory: Analysis of Conflict (1991), Harvard University Press: Harvard University Press Cambridge, MA · Zbl 0729.90092
[27] Ochs, J.; Roth, A. E., An Experimental Study of Sequential Bargaining, Amer. Econ. Rev., 79, 355-384 (1989)
[28] Prasnikar, V.; Roth, A. E., Considerations of Fairness and Strategy: Experimental Data from Sequential Games, Quart. J. Econ., 106, 865-888 (1992) · Zbl 0825.90814
[29] Roth, A. E., Bargaining Experiments, (Kagel, J.; Roth, A. E., Handbook of Experimental Economics (1994), Princeton University Press: Princeton University Press Princeton, NJ), forthcoming · Zbl 0426.90096
[30] Roth, A. E.; Erev, I., Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term (1993), University of Pittsburgh, mimeo
[31] Roth, A. E.; Prasnikar, V.; Okuno-Fujiwara, M.; Zamir, S., Bargaining and Market Power in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study, Amer. Econ. Rev., 81, 1068-1095 (1991)
[32] Samuelson, L., Evolutionary Foundations of Solution Concepts for Finite, Two-Player, Normal-Form Games, (Vardi, M. Y., Theoretical Aspects of Reasoning about Knowledge (1988), Morgan Kaufmann: Morgan Kaufmann San Mateo, CA) · Zbl 0706.90104
[33] Samuelson, L., Does Evolution Eliminate Domianted Strategies?, (Binmore, K.; Kirman, A.; Tani, P., Frontiers of Game Theory (1993), MIT Press: MIT Press Cambridge, MA) · Zbl 0808.90145
[34] Samuelson, L., Stochastic Stability in Games with Alternative Best Replies, J. Econ. Theory, 64, 35-65 (1994) · Zbl 0811.90138
[35] Samuelson, L.; Zhang, J., Evolutionary Stability in Asymmetric Games, J. Econ. Theory, 57, 363-391 (1992) · Zbl 0770.90096
[36] Schlag, K. H., Why imitate, and if so, how? (1994), University of Bonn, mimeo
[37] Selten, R., Reexamination of the Perfectness Concept for Equilibrium Points in Extensive-Form Games, Int. J. Game Theory, 4, 25-55 (1975) · Zbl 0312.90072
[38] Selten, R., The Chain-Store Paradox, Theory Dec., 9, 127-159 (1978) · Zbl 0374.90085
[39] Smith, V., Experimental Economics: Induced Value Theory, Amer. Econ. Rev., 66, 274-279 (1976)
[40] Taylor, P. D.; Jonker, L. B., Evolutionarily Stable Strategies and Game Dynamics, Math. Biosci., 40, 145-156 (1978) · Zbl 0395.90118
[41] Thaler, R. H., Anomalies: The Ultimatum Game, J. Econ. Perspect., 2, 185-206 (1988)
[42] van Damme, E., Stability and Perfection of Nash Equilibria (1987), Springer-Verlag: Springer-Verlag Berlin · Zbl 0696.90087
[43] Young, P., The Evolution of Conventions, Econometrica, 61, 57-84 (1993) · Zbl 0773.90101
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