A patient player interacts with a sequence of short-run players. The patient player is either an honest type who always takes a commitment action and never erases any record, or an opportunistic type who decides which action to take and whether to erase his action at a low cost. I show that in every equilibrium, the patient player will have an incentive to take the commitment action until he has accumulated a long enough good record, at which point he can secure a payoff that is strictly greater than his commitment payoff. However, as long as the patient player is sufficiently long-lived, his equilibrium payoff must be close to his minmax value. This is because the ability to erase records enables the opportunistic type to pool with the honest type who is younger in age. As the player's expected lifespan increases, his opponents' posterior belief will assign a lower probability to him being the honest type since the honest type is younger on average. This will lower his reputation at any history, slow down his reputation-building process, and wipe out his returns from building reputations. However, a small probability of the opportunistic type only has a negligible effect on the short-run players' welfare, which is close to their expected payoff in a repeated complete information game where the patient player's type is common knowledge.

I study repeated games with anonymous random matching where players endogenously decide whether to disclose signals about their past actions. I establish an-anti folk theorem, that when players are sufficiently long-lived, they will almost always play their dominant actions and will almost never cooperate. Then I examine whether players can sustain cooperation when their expected lifespans are intermediate and I focus on equilibria that are purifiable. I show that when players' actions are strategic complements, they cannot sustain any cooperation in any purifiable equilibria regardless of their time preference and their expected lifespans. This is because it is impossible to deliver high continuation values to players who have cooperated many times before. In contrast, when players' actions are strategic substitutes, they can sustain some cooperation in some purifiable equilibria as long as they are not too impatient and their expected lifespans belong to some intermediate range. My results imply that the maximal level of cooperation a community can sustain is not monotone with respect to its members' expected lifespans and the complementarity of players' actions can undermine their abilities to sustain cooperation.

I analyze a novel reputation game between a patient seller and a sequence of myopic consumers, in which the consumers have limited memories and do not know the exact sequence of the seller's actions. I focus on the case where each consumer only observes the number of times that the seller took each of his actions in the last K periods and players have monotone-supermodular payoffs, namely, the patient player's payoff is strictly increasing in his opponent's action and is strictly decreasing in his own action, and both players' stage-game payoff functions have strictly increasing differences. With positive probability, the seller is a commitment type that exerts high effort in every period.