Reputation in the Shadow of Exit

TL;DR

This paper examines how endogenous exit in repeated games affects reputation formation, revealing conditions under which long-term players can still achieve optimal payoffs despite the risk of permanent game termination.

Contribution

It identifies conditions for long-run players to attain Stackelberg payoffs in Markov equilibria with endogenous exit, challenging traditional reputation results.

Findings

Reputation can be rendered useless by exit in certain conditions.

Conditions are derived for long-run players to achieve Stackelberg payoffs.

Application to chain-store and global games demonstrates the theory's relevance.

Abstract

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 all 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 conditional commitment foundations for the infinite chain-store game. I also analyze repeated global games with exit, and obtain new predictions about regime survival.