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

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  • Gossner, Olivier
  • Hörner, Johannes

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.

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  • 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.
  • Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:63-84
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    Cited by:

    1. 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.
    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. Peski, Marcin & Wiseman, Thomas, 2015. "A folk theorem for stochastic games with infrequent state changes," Theoretical Economics, Econometric Society, vol. 10(1), January.
    4. Cingiz, Kutay & Flesch, Janos & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2016. "Perfect Information Games where Each Player Acts Only Once," Research Memorandum 036, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Kimmo Berg, 2017. "Extremal Pure Strategies and Monotonicity in Repeated Games," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 387-404, March.
    6. repec:eee:jetheo:v:175:y:2018:i:c:p:58-87 is not listed on IDEAS

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