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The truth behind the myth of the Folk theorem

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  • Halpern, Joseph Y.
  • Pass, Rafael
  • Seeman, Lior

Abstract

We study the problem of computing an ϵ-Nash equilibrium in repeated games. Earlier work by Borgs et al. (2010) suggests that this problem is intractable. We show that if we make a slight change to their model—modeling the players as polynomial-time Turing machines that maintain state—and make a standard cryptographic assumption (that public-key cryptography can carried out), the problem can actually be solved in polynomial time. Our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games (where, roughly speaking, which players' actions a given player's utility depends on are characterized by a graph, typically of bounded degree). As Nash equilibrium is a weak solution concept for extensive-form games, we additionally define and study an appropriate notion of subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, assuming public-key cryptography).

Suggested Citation

  • Halpern, Joseph Y. & Pass, Rafael & Seeman, Lior, 2019. "The truth behind the myth of the Folk theorem," Games and Economic Behavior, Elsevier, vol. 117(C), pages 479-498.
    • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:479-498
    DOI: 10.1016/j.geb.2019.04.008
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    References listed on IDEAS

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    1. Borgs, Christian & Chayes, Jennifer & Immorlica, Nicole & Kalai, Adam Tauman & Mirrokni, Vahab & Papadimitriou, Christos, 2010. "The myth of the Folk Theorem," Games and Economic Behavior, Elsevier, vol. 70(1), pages 34-43, September.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
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    4. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
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    9. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    10. O. Gossner, 2000. "Sharing a long secret in a few public words," THEMA Working Papers 2000-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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    Cited by:

    1. Dargaj, Jakub & Simonsen, Jakob Grue, 2023. "A complete characterization of infinitely repeated two-player games having computable strategies with no computable best response under limit-of-means payoff," Journal of Economic Theory, Elsevier, vol. 213(C).
    2. Jakub Dargaj & Jakob Grue Simonsen, 2020. "A Complete Characterization of Infinitely Repeated Two-Player Games having Computable Strategies with no Computable Best Response under Limit-of-Means Payoff," Papers 2005.13921, arXiv.org, revised Jun 2020.

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    More about this item

    Keywords

    Equilibrium Computation; Folk theorem; Repeated games; Bounded rationality;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines

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