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...

Often, perfect bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied whenever possibleʺ. We show that there are games in which it is not clear what whenever possibleʺ means. Then, we provide a simple...