Competitive Information Design with Asymmetric Senders

Abstract

We consider a competitive information design game in which a number of ex-ante asymmetric senders are competing for a receiver by disclosing information about their respective realizations. Unlike the setting with symmetric senders where a symmetric equilibrium always exists, the equilibrium may not exist under the asymmetric setting. Using the idea of discrete approximation and passing to the limit, we show that if there is no mass point in the senders' priors, then an equilibrium always exists. We next establish the necessary and sufficient conditions for the equilibrium structure. Our characterizations strictly generalize the symmetric equilibrium conditions provided in the symmetric environment studied in previous works. We then use the characterized equilibrium structure to solve the equilibrium for a general two-sender game along with providing a computational method of computing it.

Keywords: Information design, Competition, Ex-ante asymmetry, Nash equilibrium