Equilibrium restoration in a class of tolerant strategies

This study shows that in a two-player infinitely repeated game where one is impatient, Pareto-superior subgame perfect equilibrium can still be achieved. An impatient player in this paper is depicted as someone who can truly destroy the possibility of attaining any feasible and individually rational outcome that is supported in equilibrium in repeated games, as asserted by the Folk Theorem. In this scenario, the main ingredient for the restoration of equilibrium is to introduce the notion of tolerant trigger strategy. Consequently, the use of the typical trigger strategy is abandoned since it ceases to be efficient as it only brings automatically the game to its punishment path, therefore eliminating the possibility of extracting other feasible equilibria. I provide a simple characterization of perfect equilibrium payoffs under this scenario and show that cooperative outcome can be approximated.