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 who 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 who 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 of at least the commitment payoffs in each state in every equilibrium.