Abstract: This paper defines a general framework to study infinitely repeated gameswith time-dependent discounting in which we distinguish and discuss both time-consistent and -inconsistent preferences. To study the long-term properties of repeatedgames, we introduce an asymptotic condition to characterize the fact that players be-come more and more patient; that is, the discount factors at all stages uniformly con-verge to one. Two types of folk theorems are proven without the public randomizationassumption: the asymptotic one, that is, the equilibrium payoff set converges to thefeasible 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 singlestrategy profile that is an approximate subgame perfect Nash equilibrium in all gameswith sufficiently patient discount factors. We use two methods for the study of asymp-totic folk theorem: the self-generating approach and the constructive proof. We presentthe constructive proof in the perfect-monitoring case and show that it can be extendedto time-inconsistent preferences. The self-generating approach applies to the public-monitoring case but may not extend to time-inconsistent preferences because of a non-monotonicity result.

研究成果：The Folk Theorem or Repeated Games with Time-Dependent Discounting

发表期刊：MATHEMATICS OF OPERATIONS RESEARCH

论文链接：https://pubsonline.informs.org/doi/epdf/10.1287/moor.2021.1183