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

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Author Info
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.

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Paper provided by EconWPA in its series Game Theory and Information with number 9312003.

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Date of creation: 14 Dec 1993
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Handle: RePEc:wpa:wuwpga:9312003

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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  1. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
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  2. 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. [Downloadable!] (restricted)
  3. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
  4. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March. [Downloadable!] (restricted)
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  5. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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  7. Smale, Steve, 1980. "The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games," Econometrica, Econometric Society, vol. 48(7), pages 1617-34, November. [Downloadable!] (restricted)
  8. Vincent Crawford, 1992. "Adaptive Dynamics in Coordination Games," University of California at San Diego, Economics Working Paper Series 92-02r, Department of Economics, UC San Diego.
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  9. Rubinstein, Ariel, 1986. "Finite automata play the repeated prisoner's dilemma," Journal of Economic Theory, Elsevier, vol. 39(1), pages 83-96, June. [Downloadable!] (restricted)
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