Noisy signaling in discrete time

Abstract

This paper characterizes the equilibrium set of a dynamic noisy-signaling model in discrete time. A seller privately knows the quality of her asset. She can exert a costly effort to generate stochastic returns. Buyers stochastically arrive over time and, after observing the history of returns, they make price offers. In our model, the equilibrium behavior of the buyers is discontinuous: they only make acceptable (high) offers if the posterior about the quality is above a given threshold. As a result, the recursive nature of the model replicates the discontinuity, giving the equilibrium continuation payoff a complex self-replicating structure that may take the form of a devil’s staircase.