Bounded Rationality in Repeated Games∗

Models of bounded rationality often lead to sharper predictions about real world outcomes than their full rationality counterparts. Full rationality in repeated interactions allows a plethora of equilibrium outcomes. In this paper, I examine the effect of bounded rationality in infinitely repeated games. In particular, does the introduction of boundedly rational agents lead to a smaller set of outcomes in equilibrium? I show that the number of equilibrium outcomes is smaller when agents are boundedly rational. Importantly, cooperative outcomes are still possible in equilibrium, even when players can’t use sophisticated strategies and are not able to perfectly monitor their opponents. The strategy that leads to cooperation is called “Win-Stay, Lose-Shift”. Using this strategy, I show that cooperation is possible in equilibrium for a large class of 2x2 games. I also give necessary and sufficient conditions on equilibrium structure for twoplayer N ×M games. These conditions suggest that in equilibrium, players must be able to cooperate without getting caught in long periods of conflict. JEL classification: C62,C72,C73