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A Bounded Rationality, Evolutionary Model for Behavior in Two Person Reciprocity Games

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  • Jeffrey E. Prisbrey

    (Universitat Pompeu Fabra)

Abstract

Standard non-cooperative game theory is not selective enough to discriminate among many of the possible outcomes in infinitely repeated reciprocity games. However, experimental evidence, especially in symmetric games, suggests strongly that people arrive at only a few outcomes. Theoretical justification for these particular outcomes is usually derived from focal and axiomatic solution concepts, yet these procedures are inherently ad-hoc. Here the outcome of a population game with evolutionary dynamics is examined in order to theatrically justify experimentally observed behavior in a less ad-hoc manner. It is shown that under an assumption of limited rationality, specifically limited memory, there is a unique global equilibrium in the Replicator Dynamics. The unique equilibrium contains a trio of outcomes: non-cooperative Nash play, payoff irrational play, and cooperative turn-taking, which roughly match the outcomes observed experimentally.

Suggested Citation

  • Jeffrey E. Prisbrey, 1993. "A Bounded Rationality, Evolutionary Model for Behavior in Two Person Reciprocity Games," Game Theory and Information 9312003, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpga:9312003
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    References listed on IDEAS

    as
    1. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers 11-8-2, Pennsylvania State - Department of Economics.
    2. Banks, Jeffrey S. & Sundaram, Rangarajan K., 1990. "Repeated games, finite automata, and complexity," Games and Economic Behavior, Elsevier, vol. 2(2), pages 97-117, June.
    3. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    4. Smale, Steve, 1980. "The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games," Econometrica, Econometric Society, vol. 48(7), pages 1617-1634, November.
    5. Jack Hirshleifer & Juan Carlos Martinez Coll, 1988. "What Strategies Can Support the Evolutionary Emergence of Cooperation?," Journal of Conflict Resolution, Peace Science Society (International), vol. 32(2), pages 367-398, June.
    6. Gilboa, Itzhak & Samet, Dov, 1989. "Bounded versus unbounded rationality: The tyranny of the weak," Games and Economic Behavior, Elsevier, vol. 1(3), pages 213-221, September.
    7. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    8. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    9. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June.
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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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