On the limit perfect public equilibrium payoff set in repeated and stochastic games

Abstract

This paper provides a dual characterization of the existing ones for the limit set of perfect public equilibrium payoffs in a class of finite stochastic games (in particular, repeated games) as the discount factor tends to one. As a first corollary, the folk theorems of Fudenberg et al. (1994), Kandori and Matsushima (1998) and Hörner et al. (2011) obtain. As a second corollary, it is shown that this limit set of payoffs is a convex polytope when attention is restricted to perfect public equilibria in pure strategies. This result fails for mixed strategies, even when attention is restricted to two-player repeated games.

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Reference

Johannes Hörner, Satoru Takahashi, and Nicolas Vieille, “On the limit perfect public equilibrium payoff set in repeated and stochastic games”, Games and Economic Behavior, vol. 85, 2014, pp. 70–83.