Cooperation and Community Responsibility: A Folk Theorem for Repeated Matching Games with Names

Abstract

When large communities transact with each other and players change rivals over time, players may not recognize each other or may have limited information about past play. Can players cooperate in such anonymous transactions? I analyze an infinitely repeated random matching game between two communities. Players' identities are unobservable and players only observe the outcomes of their own matches. Players may send an unverifiable message (a name) before playing each game. I show that for any such game, all feasible individually rational payoffs can be sustained in equilibrium if players are sufficiently patient. Cooperation is achieved not by the standard route of community enforcement or third-party punishments, but by community responsibility. If a player deviates, her entire community is held responsible and punished by the victim.