Repeated Games with Endogenous Discounting

In a symmetric repeated game with standard preferences, there are no gains from intertemporal trade. In fact, under a suitable normalization of utility, the payoff set in the repeated game is identical to that in the stage game. We show that this conclusion may no longer be true if preferences are recursive and stationary, but not time separable. If so, the players’ rates of time preference are no longer fixed, but may vary endogenously, depending on what transpires in the course of the game. This creates opportunities for intertemporal trade, giving rise to new and interesting dynamics. For example, the efficient and symmetric outcome of a repeated prisoner’s dilemma may be to take turns defecting, even though the efficient and symmetric outcome of the stage game is to cooperate. A folk theorem shows that such dynamics can be sustained in equilibrium if the players are sufficiently patient.