Sustainable reputations with rating systems

We study a class of moral hazard games between a long lived agent and an in nite sequence of short lived principals. We assume that principals cannot observe past signals. To facilitate the analysis of applications such as online auctions (e.g. eBay), online shopping search engines (e.g. BizRate.com) and consumer reports, we assume that a central mechanism observes all past signals, and makes public announcements every period. The set of announcements and the mapping from observed signals to the set of announcements is called a rating system. We show that absent reputation effects, information censoring cannot improve attainable payoffs. However, if there is an initial probability that the agent is a commitment type that plays a particular strategy every period, then there exists a rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the agent is almost his Stackelberg payoff after every history. This is in contrast to Cripps, Mailath and Samuelson (2004), where it is shown that reputation effects do not last long in such games if principals can observe all past signals. We also construct rating systems that increase payoffs of almost all principals, while decreasing the agent's payoff. I am indebted to Faruk Gul for guidance at every stage of this work. I am also grateful for suggestions and comments to Wioletta Dziuda, Aytek Erdil, Gabor Virag and Andrea Wilson. All remaining errors are my own. yDepartment of Economics, Fisher Hall, Princeton, NJ 08544. E-mail: [email protected].