Stochastic Stability in Finitely Repeated Two Player Games

Abstract

I apply Kandori, Mailath and Rob (Econometrica, 1993) evolutionary dynamic to undiscounted finitely repeated two player games, without common interests. I find an Evolutionary “Folk Theorem” under slightly more restrictive conditions that are required for a standard “Folk Theorem” (Benoit and Krishna, Econometrica, 1985). Specifically I demonstrate that as repetitions go to infinity, the set of stochastically stable equilibrium payoff converges to the set of individually rational and feasible payoffs. However, to show this I assume that the stage game is weakly acyclic and has a pair of Pareto ranked Nash equilibria, one of which yields each player his minimax. It is demonstrated that the stochastically stable equilibria are stable as a set, but unstable as individual equlibria. Consequently an evolutionary folk theorem can make no prediction more specific than the entire individually rational and feasible set.

Keywords: Stability, Repeated games, Finite repetition, Games, Folk Theorem, Nash equilibria, Pareto efficiency

JEL Classification: C73