On the behavior of separating equilibria of signaling games with a finite set of types as the set of types becomes dense in an interval

Abstract

While signaling models with a continuum of types have well-determined (often unique) separating equilibria, models with a finite set of types do not. For signaling games, the following is proved: Suppose there is a sequence of finite sets of types, each set refining its predecessor and the limit set dense in an interval. Then every sequence of separating equilibrium paths has a convergent subsequence, the limit of any convergent sequence is a separating equilibrium path of the limit game, and the convergence is uniform. If the limit game has a unique equilibrium path then every sequence converges to it. Show more