Uniform Folk Theorems in Repeated Anonymous Random Matching Games

Abstract

We study infinitely repeated anonymous random matching games played by communities of players, who only observe the outcomes of their own matches. It is well known that cooperation can be sustained in equilibrium for the prisoner’s dilemma (PD) through grim trigger strategies. Little is known about games beyond the PD. We study a new equilibrium concept, strongly uniform equilibrium (SUE, which refines the notion of uniform equilibrium (UE) and has additional properties such as a strong version of (approximate) sequential rationality. We establish folk theorems for general games and arbitrary number of communities. Interestingly, the equilibrium strategies we construct are easy to play. We extend the results to a setting with imperfect private monitoring, for the case of two communities. We also show that it is possible for some players to get equilibrium payoffs that are outside the set of individually rational and feasible payoffs of the stage game. In particular, for the PD we derive a bound on the number of “free-riders” that can be sustained in society. A by-product of our analysis is an important result relating uniform equilibrium and strongly uniform equilibria: we show that, in general repeated games with finite players, actions, and signals, the set of UE and SUE payoffs coincide.

Keywords: anonymous random matching; uniform equilibria; repeated games