Robustness of Reputation Effects under Uncertain Monitoring

I study reputation effects under uncertain monitoring. I examine a repeated game between a long-run player and a series of short-run opponents. The long-run player can either be a strategic type or a commitment type that plays the same action in every period. The modeling innovation is that the short-run player is unsure about the monitoring structure. The uncertainty about the monitoring structure introduces new challenges to reputation building because there may not be a direct relationship between the distribution of signals and the long-run player's strategy. Thus the long-run player may not have the ability to establish a reputation for commitment. I show that, when the short-run players cannot statistically distinguish commitment action from a bad action, the standard reputation results break down. I also provide sufficient conditions under which reputation effects on long-run player’s payoffs can be extended to the current framework. When the commitment payoff is the highest payoff he can get, the conditions can be relaxed.