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Behavior-Dependent Contexts for Repeated Plays of the Prisoner's Dilemma

Author

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  • Ewart A. C. Thomas

    (Department of Psychology, Stanford University)

  • Marcus W. Feldman

    (Department of Biological Sciences, Stanford University)

Abstract

This article analyzes the game-theoretic stability of three strategies, Tit-For-Tat (TFT), all-Defect (all-D), and all-Cooperate (all-C), that actors might use for repeated plays of the Prisoner's Dilemma (PD). The probability that there will be a next play is assumed to depend on the current behavior of one of the actors—it is w after cooperation and u after a defection—and two cases are examined. The first case is where an actor assumes that the continuation probability depends on its own behavior, and the second is where the continuation probability is assumed to depend on the other actor's behavior. It is shown that the potential for mutual cooperation is higher in the first case than in the second. A detailed examination of the first case reveals that when the ratio (1 - w )/(1 - u ) is sufficiently extreme for certain classes of PD, the “cooperative†strategy TFT is stable and the “noncooperative†strategy all-D is unstable. For these classes of PD, it is thus possible both for cooperation to be maintained once it is established, and for cooperation to become established in a world of defectors. The sensitivity of these results to the precision in measurement of payoffs and probabilities is discussed.

Suggested Citation

  • Ewart A. C. Thomas & Marcus W. Feldman, 1988. "Behavior-Dependent Contexts for Repeated Plays of the Prisoner's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 32(4), pages 699-726, December.
    • Handle: RePEc:sae:jocore:v:32:y:1988:i:4:p:699-726
    DOI: 10.1177/0022002788032004005
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    References listed on IDEAS

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    1. Axelrod, Robert, 1981. "The Emergence of Cooperation among Egoists," American Political Science Review, Cambridge University Press, vol. 75(2), pages 306-318, June.
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    Cited by:

    1. Lucas Wardil & Marco Antonio Amaral, 2017. "Cooperation in Public Goods Games: Stay, But Not for Too Long," Games, MDPI, vol. 8(3), pages 1-10, August.
    2. Kurokawa, Shun & Zheng, Xiudeng & Tao, Yi, 2019. "Cooperation evolves more when players keep the interaction with unknown players," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 209-216.
    3. Qu, Xinglong & Zhou, Changli & Cao, Zhigang & Yang, Xiaoguang, 2016. "Conditional dissociation as a punishment mechanism in the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 215-223.

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