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We study community enforcement in a large population with noisy monitoring. We focus on equilibria in the prisoner’s dilemma that are coordination proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by the equilibrium continuation payoffs at their current histories. We show that a noise-tolerant version of contagion strategies is optimal among all coordination-proof equilibria. Welfare under tolerant contagion strategies decreases in the noise level and the gain from defection faster than welfare in a fixed partnership does. Thus, community enforcement has a comparative advantage in supporting “ low-stakes”relationships. (JEL C72, C73, C78, Z13) 

Abstract We introduce a new model of repeated games in large populations with random matching, overlapping generations, and limited records of past play. We prove that steady-state equilibria exist under general conditions on records. When the updating of a player’s record can depend on the actions of both players in a match, any strictly individually rational action can be supported in a steady-state equilibrium. When record updates can depend only on a player’s own actions, fewer actions can be supported. Here, we focus on the prisoner’s dilemma and restrict attention to strict equilibria that are coordination-proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by their records and expected continuation payoffs. Such equilibria can support full cooperation if the stage game is either “strictly supermodular and mild” or “strongly supermodular,” and otherwise permit no cooperation at all. The presence of “supercooperator” records, where a player cooperates against any opponent, is crucial for supporting any cooperation when the stage game is “severe.”