Reputation Effects with Endogenous Records

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 that action from his record at a low cost. We show that the patient player will have an incentive to build a reputation in every equilibrium and can secure a payoff that is strictly greater than his commitment payoff after accumulating a long enough good record. However, as long as the patient player has a sufficiently long lifespan, his equilibrium payoff must be close to his minmax value. Although a small probability of opportunistic type can wipe out all of the patient player’s returns from building reputations, it only has a negligible effect on the short-run players’ welfare.