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Recursive Methods in Discounted Stochastic Games: An Algorithm for ! ! 1 and a Folk Theorem

Author

Listed:
  • Johannes Horner

    (Yale University)

  • Takuo Sugaya

    (Princeton University)

  • Satoru Takahashi

    (Princeton University)

  • Nicolas Vieille

    (HEC Paris)

Abstract
We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players?) equilibrium payoffs is independent of the initial state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period?s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.

Suggested Citation

  • Johannes Horner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2010. "Recursive Methods in Discounted Stochastic Games: An Algorithm for ! ! 1 and a Folk Theorem," Working Papers 1264, Princeton University, Department of Economics, Econometric Research Program..
    • Handle: RePEc:pri:metric:wp005.pdf
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    References listed on IDEAS

    as
    1. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    4. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    5. 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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    Cited by:

    1. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
    2. Escobar, Juan F. & Llanes, Gastón, 2018. "Cooperation dynamics in repeated games of adverse selection," Journal of Economic Theory, Elsevier, vol. 176(C), pages 408-443.

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    More about this item

    Keywords

    stochastic games;

    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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