Disappearance of reputations in two-sided incomplete-information games

•This paper examines the sustainability of reputations in games with two long-lived players.•Each player may be a normal or a commitment type who plays the Stackelberg action.•Both players know their own type but not the types of the other player.•We consider a class of games, with one-sided moral hazard, under imperfect public monitoring.•Neither player can sustain reputation permanently for a noncredible behavior in these games.

This paper examines the sustainability of 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 economic interactions that may involve hidden-information or hidden-action. Extending the techniques of Cripps et al. (2004), it is found that neither player can sustain a reputation permanently for playing a noncredible behavior in these games; and, the reputations disappear uniformly across all Nash equilibria.