The Folk Theorem for Repeated Games with Time-Dependent Discounting

Daehyun Kim () and Xiaoxi Li ()
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Daehyun Kim: Economics and Management School of Wuhan University, Wuhan 430072, China
Xiaoxi Li: Economics and Management School of Wuhan University, Wuhan 430072, China

Mathematics of Operations Research, 2022, vol. 47, issue 2, 1631-1647

Abstract: This paper defines a general framework to study infinitely repeated games with time-dependent discounting in which we distinguish and discuss both time-consistent and -inconsistent preferences. To study the long-term properties of repeated games, we introduce an asymptotic condition to characterize the fact that players become more and more patient; that is, the discount factors at all stages uniformly converge to one. Two types of folk theorems are proven without the public randomization assumption: the asymptotic one, that is, the equilibrium payoff set converges to the feasible and individual rational set as players become patient, and the uniform one, that is, any payoff in the feasible and individual rational set is sustained by a single strategy profile that is an approximate subgame perfect Nash equilibrium in all games with sufficiently patient discount factors. We use two methods for the study of asymptotic folk theorem: the self-generating approach and the constructive proof. We present the constructive proof in the perfect-monitoring case and show that it can be extended to time-inconsistent preferences. The self-generating approach applies to the public-monitoring case but may not extend to time-inconsistent preferences because of a nonmonotonicity result.

Keywords: Primary: 91A20; secondary: 91B06; repeated games; folk theorem; perfect public equilibrium; subgame perfect Nash equilibrium; time-dependent discounting; time-inconsistency; public monitoring (search for similar items in EconPapers)
Date: 2022
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