Sustainable reputations with rating systems

In a product choice game played between a long lived seller and an infinite sequence of buyers, we assume that buyers 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 seller is a commitment type that plays a particular strategy every period, then there exists a finite rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the seller 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 forever in such games if buyers can observe all past signals. We also construct finite rating systems that increase payoffs of almost all buyers, while decreasing the seller's payoff.