Patience or Fairness? Analyzing Social Preferences in Repeated Games

This paper investigates how the introduction of social preferences affects players’ equilibrium behavior in both one-shot and infinitely repeated versions of the Prisoner’s Dilemma game. We first show that defection survives as the unique equilibrium of the stage game if at least one player is not too concerned about inequity aversion. Second, we demonstrate that in the infinitely repeated version of the game, fairness concerns operate as a “substitute: for time discounting, as fairness helps sustain cooperation for lower discount factors. We then extend our results to more general simultaneous-move games, and more general preferences. Furthermore, we examine how the introduction of incomplete information about players’ social preferences can help in the selection of the efficient cooperative outcome. Finally, we point out the implications of our findings for the design and analysis of experiments involving repeated games. In particular, repeated game equilibria which are thought to be supported by sufficiently large discount factors, may in fact be sustained by a combination of discounting and social preference parameters, an observation that may help rationalize recent experimental findings.