Disappearing private reputations in long-run relationships

• Published in: Journal of economic theory Vol. 134; no. 1; pp. 287 - 316
• Main Authors: Cripps, Martin W., Mailath, George J., Samuelson, Larry
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01-05-2007; Elsevier; Elsevier Science Publishing Company, Inc
• Series: Journal of Economic Theory
• Subjects: Beliefs; Commitment; Economic theory; Game theory; Imperfect monitoring; Monitoring; Private beliefs; Repeated games; Reputation; Reputations; Studies; Uncertainty; Repeated games; C78; Reputation; Commitment; C70; Private beliefs; Imperfect monitoring
• ISSN: 0022-0531; 1095-7235
• DOI: 10.1016/j.jet.2006.03.007

For games of
public reputation with uncertainty over types and imperfect public monitoring, Cripps et al. [Imperfect monitoring and impermanent reputations, Econometrica 72 (2004) 407–432] showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is
not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is
private. The rate at which reputations disappear is uniform across equilibria and reputations also disappear in sufficiently long discounted finitely repeated games.