Reputation building under uncertain monitoring

We study the standard reputation model with a long-run (LR) player facing a sequence of short-run (SR) opponents, with one difference: the SR players are uncertain about the monitoring structure, while the LR player knows it. We construct examples where the standard reputation result breaks down: Even if there is a possibility that the LR player is a commitment type that always plays the action to which he wants to commit, there exist ``bad'' equilibria in which the LR player gets payoffs substantially lower than his commitment payoffs. In contrast, if there is the possibility of dynamic commitment types that switch between ``signaling'' actions that help the SR players learn the monitoring structure and ``collection'' actions that are desirable for payoffs, our main theorem shows that a sufficiently patient LR player obtains payoffs at least the commitment payoffs in each state in every equilibrium.