Disappearance of reputations in two-sided incomplete-information games

This paper studies long-run sustainability of false reputations 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. This class, namely reputation games with one-sided moral hazard, can capture a wide range of economic interactions between two parties that may involve hidden-information or hidden-action. Extending the techniques of Cripps, Mailath, and Samuelson (2004), it is found that neither player can sustain a false reputation permanently for playing a noncredible behavior in these games; and, false reputations disappear sequentially and uniformly across all Nash equilibria. Moreover, it is shown that this is the only class (with simple commitment types) for which the true types of both players are sequentially revealed in all Nash equilibria in the long-run. To do so, we construct a Nash equilibrium in a reputation game with two-sided moral hazard where both false reputations are maintained indefinitely. Journal of Economic Literature Classification Numbers: C70; C73.