Reputation in the Shadow of Exit

Abstract

I study reputation formation when player actions endogenously determine the probability the game permanently ends. Exit can render reputation useless even to a patient player whose actions are perfectly monitored, in contrast to canonical commitment payoff theorems. However, I identify conditions for the long-run player to attain their Stackelberg payoff in all Markov equilibria. Along the way, I highlight the role Markov strategies play in pinning down the value of reputation. 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.