Reputation Effects in Two-Sided Incomplete-Information Games

This paper studies reputation effects in a class of games with imperfect public monitoring and two long-lived players, both of whom have private information about their own type and uncertainty over the types of the other player. Players may be either a strategic type who maximizes expected utility or a (simple) commitment type who plays a prespecified action every period. As in standard models, the reputation of a strategic type of player for being the commitment type is established by mimicking the behavior of the commitment type. The distinct feature of our model is that both strategic players aim to establish a (false) reputation for being the commitment type. The class of games we consider encompasses a wide range of economic interactions between two parties that involve hiddeninformation (e.g. between a regulator and a regulatee) or hidden-action (e.g between an employer and an employee), where the reputation concerns of both parties are apparent. In both games, one party (principal) prefers that the other party (agent) play in a specific way and use costly auditing to enforce this behavior. The principal aims to establish a reputation for being diligent; whereas the agent want to build a reputation for being virtuous. Extending the techniques of Cripps, Mailath, and Samuelson (2004), we find that neither strategic player can sustain a reputation for playing a noncredible behavior, i.e. a behavior which is not optimal given that the opponent is best responding in the stage game. Hence, in this class, the true types of both players will be revealed eventually in all Nash equilibria and the asymmetric information does not affect equilibrium analysis in the long-run. In fact, we show that this is the only class of two-sided incomplete information games (with simple commitment types) where reputations disappear in the long-run, in all equilibria. To do so, we provide an example where reputations for noncredible behavior are sustained in a Nash equilibrium. ∗I am grateful to my advisor Aldo Rustichini for his invaluable guidance and encouragement throughout this project. I also thank Chris Phelan and Jan Werner for their very helpful comments and support. In addition, I thank Rajesh Aggarwal, Beth Allen, Ioanna Grypari, David Rahman, Gina Pieters, Itai Sher, Yuichiro Waki, Randall Wright and participants of Mathematical Economics Workshop at the University of Minnesota, seminars at Bogazici University, Middle East Technical University, Bilkent University and TOBB-ETU for their comments and suggestions. Financial support from Graduate Research Partnership Program Fellowship is gratefully acknowledged. All remaining errors are mine. Email [email protected] for comments and questions.