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Bounded computational capacity equilibrium

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  • Hernández, Penélope
  • Solan, Eilon

Abstract

A celebrated result of Abreu and Rubinstein (1988) states that in repeated games, when the players are restricted to playing strategies that can be implemented by finite automata and they have lexicographic preferences, the set of equilibrium payoffs is a strict subset of the set of feasible and individually rational payoffs. In this paper we explore the limitations of this result. We prove that if memory size is costly and players can use mixed automata, then a folk theorem obtains and the set of equilibrium payoffs is once again the set of feasible and individually rational payoffs. Our result emphasizes the role of memory cost and of mixing when players have bounded computational power.

Suggested Citation

  • Hernández, Penélope & Solan, Eilon, 2016. "Bounded computational capacity equilibrium," Journal of Economic Theory, Elsevier, vol. 163(C), pages 342-364.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:342-364
    DOI: 10.1016/j.jet.2016.02.007
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    Cited by:

    1. Misha Gavrilovich & Victoria Kreps, 2018. "Games with Symmetric Incomplete Information and Asymmetric Computational Resources," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-16, June.
    2. O. V. Baskov, 2019. "Equilibrium payoffs in repeated two-player zero-sum games of finite automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 423-431, June.

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    More about this item

    Keywords

    Bounded rationality; Automata; Complexity; Infinitely repeated games; Equilibrium;
    All these keywords.

    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

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