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

• 成果类型: Article
• 署名作者: Gossner, Olivier; Hoerner, Johannes
• 署名单位: Paris School of Economics; University of London; London School Economics & Political Science; Yale University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2009.07.002
• 发表日期: 2010
• 页码: 63-84
• 关键词: Folk theorem; Repeated game; Individually rational payoff; Min max payoff; signals; entropy; conditional independence

摘要

We study the relationship between a player's lowest equilibrium payoff in a repeated game with imperfect monitoring and this player's min max payoff in the corresponding one-shot game. We characterize the signal structures under which these two payoff's 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. (C) 2009 Elsevier Inc. All rights reserved.