Reputation with stopping time decision

Abstract

This paper studies a long run relationship between two players while one player has reputation concern and the other player's decision is a stopping time. The equilibrium structure depends on the value of the long run relationship: when the value of the relationship is low, a simple threshold equilibrium is the unique equilibrium; when the value becomes higher, a probationary period endogenously arises when reputation is in an intermediate region. Reputation concern also has discipline effect, moral hazard problem is mitigated when player's reputation becomes worse, and the discipline effect is dominating when reputation is sufficiently bad.