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A folk theorem for stochastic games with infrequent state changes

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    (Department of Economics, University of Toronto)

  • ,

    (Department of Economics, University of Texas at Austin)

Abstract

We characterize perfect public equilibrium payoffs in dynamic stochastic games, in the case where the length of the period shrinks, but players' rate of time discounting and the transition rate between states remain fixed. We present a meaningful definition of the feasible and individually rational payoff sets for this environment, and we prove a folk theorem under imperfect monitoring. Our setting differs significantly from the case considered in previous literature (Dutta (1995), Fudenberg and Yamamoto (2011), and Hörner, Sugaya, Takahashi, and Vieille (2011)) where players become very patient. In particular, the set of equilibrium payoffs typically depends on the initial state.

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  • , & ,, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    • Handle: RePEc:the:publsh:1512
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    References listed on IDEAS

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    1. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "The folk theorem for irreducible stochastic games with imperfect public monitoring," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1664-1683, July.
    2. Olivier Gossner & Johannes Hörner, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," PSE-Ecole d'économie de Paris (Postprint) halshs-00754488, HAL.
    3. Drew Fudenberg & David K. Levine, 2008. "Continuous time limits of repeated games with imperfect public monitoring," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 17, pages 369-388, World Scientific Publishing Co. Pte. Ltd..
    4. Dutta Prajit K., 1995. "A Folk Theorem for Stochastic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 1-32, June.
    5. Gossner, Olivier & Hörner, Johannes, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 63-84, January.
    6. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    7. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    8. Johannes Hörner & Takuo Sugaya & Satoru Takahashi & Nicolas Vieille, 2011. "Recursive Methods in Discounted Stochastic Games: An Algorithm for δ→ 1 and a Folk Theorem," Econometrica, Econometric Society, vol. 79(4), pages 1277-1318, July.
    9. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Cited by:

    1. Gregorio Curello, 2024. "Incentives for Collective Innovation," CRC TR 224 Discussion Paper Series crctr224_2024_566, University of Bonn and University of Mannheim, Germany.
    2. Johannes Hörner & Satoru Takahashi & Nicolas Vieille, 2015. "Truthful Equilibria in Dynamic Bayesian Games," Econometrica, Econometric Society, vol. 83(5), pages 1795-1848, September.
    3. Dutta, Prajit K. & Siconolfi, Paolo, 2019. "Asynchronous games with transfers: Uniqueness and optimality," Journal of Economic Theory, Elsevier, vol. 183(C), pages 46-75.
    4. Curello, Gregorio, 2023. "Incentives for Collective Innovation," VfS Annual Conference 2023 (Regensburg): Growth and the "sociale Frage" 277708, Verein für Socialpolitik / German Economic Association.
    5. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    6. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.

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    More about this item

    Keywords

    Stochastic games; 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

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