Chiara Margaria (Boston University)

“A Signaling Approach to Reputation”

Abstract. We study reputation dynamics in a class of continuous-time signaling models with one-sided incomplete information. Public signals about the informed player’s type and his action are distorted by a Brownian noise. We show that all public perfect equilibria are Markov in the belief of the uninformed player and provide an equilibrium characterization as a solution to a system of ordinary differential equations for any fixed discount rate. In contrast to a setup with a commitment type, reputational incentives depend on the equilibrium behavior of the two types of informed players. In our setup, reputation is temporary: in any equilibrium, the type of the informed player is eventually revealed almost surely. We apply our characterization to a Cournot duopoly and investigate the behavior of a leader who knows the demand and engages in predatory behavior; we show that the value of reputation is non-monotone in the uninformed player’s belief.