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Bounded memory Folk Theorem

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  • Barlo, Mehmet
  • Carmona, Guilherme
  • Sabourian, Hamid

Abstract

We show that the Folk Theorem holds for n-player discounted repeated games with bounded memory (recall) strategies. Our main result demonstrates that any payoff profile that exceeds the pure minmax payoff profile can be approximately sustained by a pure strategy finite memory subgame perfect equilibrium of the repeated game if the players are sufficiently patient. We also show that the result can be extended to any payoff profile that exceeds the mixed minmax payoff profile if players can randomize at each stage of the repeated game. Our results requires neither time-dependent strategies, nor public randomization, nor any communication. The type of strategies we employ to establish our result turn out to have new features that may be important in understanding repeated interactions.

Suggested Citation

  • Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2016. "Bounded memory Folk Theorem," Journal of Economic Theory, Elsevier, vol. 163(C), pages 728-774.
  • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:728-774
    DOI: 10.1016/j.jet.2016.03.001
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    References listed on IDEAS

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    More about this item

    Keywords

    Repeated games; Memory; Bounded rationality; Folk Theorem;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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