Title: Community Enforcement with Endogenous Records

Abstract: I study repeated games with anonymous random matching where players can erase signals from their records. When players are sufficiently long-lived and have strictly dominant actions, they will play their dominant actions with probability close to one in all equilibria. When players' expected lifespans are intermediate, there exist purifiable equilibria with a positive level of cooperation in the submodular prisoner's dilemma but not in the supermodular prisoner's dilemma. Therefore, the maximal level of cooperation a community can sustain is not monotone with respect to players' expected lifespans and the complementarity in players' actions can undermine their abilities to sustain cooperation.