Reputation in the Shadow of Exit

I study reputation formation in repeated games where player actions endogenously determine the probability the game permanently ends. Permanent exit can render reputation useless even to a patient long-lived player whose actions are perfectly monitored, in stark contrast to canonical commitment payoff theorems. However, I identify tight conditions for the long-run player to attain their Stackelberg payoff in the unique Markov equilibrium. Along the way, I highlight the role of Markov strategies in pinning down the value of reputation formation. I apply my results to give qualified commitment foundations for the infinite chain-store game. I also analyze repeated global games with exit, and obtain new predictions about regime survival.