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

Olivier Gossner and Johannes Hörner
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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 nationale des ponts et chaussées - 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 nationale des ponts et chaussées - 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: Yale University [New Haven]

PSE-Ecole d'économie de Paris (Postprint) from HAL

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.

Keywords: Folk theorem; Repeated game; Individually rational payoff; Minmax payoff; Signals; Entropy; Conditional independence (search for similar items in EconPapers)
Date: 2010-01
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Citations: View citations in EconPapers (5)

Published in Journal of Economic Theory, 2010, 145 (1), pp.63-84. ⟨10.1016/j.jet.2009.07.002⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-00754488

DOI: 10.1016/j.jet.2009.07.002

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