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When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?

Author

Listed:
  • Olivier Gossner

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, LSE - London School of Economics and Political Science)

  • Johannes Hörner

    (Department Economics - Yale University - Yale University [New Haven])

Abstract

We study the relationship between a player's lowest equilibrium payoff in a repeated game with imperfect monitoring and this player's minmax payoff in the corresponding one-shot game. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under an identifiability assumption, we further show that, if the monitoring structure of an infinitely repeated game "nearly" satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:pseptp:halshs-00754488
    DOI: 10.1016/j.jet.2009.07.002
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    Citations

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    Cited by:

    1. Ghislain-Herman Demeze-Jouatsa, 2020. "A complete folk theorem for finitely repeated games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1129-1142, December.
    2. Deb, Joyee & González-Díaz, Julio & Renault, Jérôme, 2016. "Uniform folk theorems in repeated anonymous random matching games," Games and Economic Behavior, Elsevier, vol. 100(C), pages 1-23.
    3. , & ,, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    4. Sugaya, Takuo & Wolitzky, Alexander, 2018. "Bounding payoffs in repeated games with private monitoring: n-player games," Journal of Economic Theory, Elsevier, vol. 175(C), pages 58-87.
    5. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.

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