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Same Game, New Tricks

Author

Listed:
  • Andrzej Pelc

    (Département d'informatique Université du Québec en Outaouais, Gatineau, Québec)

  • Krzysztof J. Pelc

    (Department of Government Georgetown University, Washington, D.C.)

Abstract

The aim of this article is to distinguish between strategies in the Iterated Prisoner’s Dilemma on the basis of their relative performance in a given population set. We first define a natural order on such strategies that disregards isolated disturbances, by using the limit of time-average payoffs. This order allows us to consider one strategy as strictly better than another in some population of strategies. We then determine a strategy σ to be ‘‘robust,’’ if in any population consisting of copies of two types of strategies, σ itself and some other strategy τ, the strategy σ is never worse than τ. We present a large class of such robust strategies. Strikingly, robustness can accommodate an arbitrary level of generosity, conditional on the strength of subsequent retaliation; and it does not require symmetric retaliation. Taken together, these findings allow us to design strategies that significantly lessen the problem of noise, without forsaking performance. Finally, we show that no strategy exhibits robustness in all population sets of three or more strategy types.

Suggested Citation

  • Andrzej Pelc & Krzysztof J. Pelc, 2009. "Same Game, New Tricks," Journal of Conflict Resolution, Peace Science Society (International), vol. 53(5), pages 774-793, October.
    • Handle: RePEc:sae:jocore:v:53:y:2009:i:5:p:774-793
    DOI: 10.1177/0022002709339045
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    References listed on IDEAS

    as
    1. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
    2. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
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