The dynamics of reputations

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Abstract
We study the endogenous dynamics of reputations in a system consisting of firms with long horizons that provide goods or services with varying levels of quality, and large numbers of customers who assign to them reputations on the basis of the quality levels that they experience when interacting with them. We show that for given discounts of the past on the part of the customers, and of effort levels on the part of the firms, the dynamics can lead to either well defined equilibria or persistent nonlinear oscillations in the number of customers visiting a firm, implying unstable reputations. We establish the criteria under which equilibria are stable and also show the existence of large transients which can also render fixed points unattainable within reasonable times. Moreover we establish that the timescales for the buildup and decay of reputations in the case of private information are much longer that those involving public information. This provides a plausible explanation for the rather sudden increase and collapse of reputations in a number of much publicized cases.

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