Competitive Equilibrium and Reputation under Imperfect Public Monitoring

In this paper we analyze a reputation-based mechanism that sustains the provision of high quality in a market for an experience good. In contrast to existing models of reputation, however, we consider a competitive market: there is a continuum of firms, each serving at most one consumer each period. We assume a perpetual probability of type replacement and imperfect public monitoring, and we analyze the evolution of firms' reputations in the high quality equilibrium. We find that there is an invariant long run distribution of firms' reputations: each firm's reputation changes every period even in the long run, but the population distribution of reputations remains constant. We consider the long run distribution of firms' reputations to further characterize the steady-state high quality equilibrium. In the equilibrium of the stage game firms with a higher reputation charge a higher price. Furthermore, we show that if the cost of high quality is decreasing in some consumer's characteristic, then buyers pay personalized prices in equilibrium.