Reputation in the Shadow of Exit

Abstract

I study reputation formation when player actions endogenously determine the prob- ability the game permanently ends. Exit can render reputation useless even when (1) players do not discount the future and (2) the Stackelberg payoff is large, in contrast to canonical commitment payoff theorems. However, I identify conditions for the long-run player to attain at least 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.