Sequential Bayesian persuasion

Abstract

I study a Bayesian persuasion model in which multiple senders sequentially persuade one receiver, after observing signal structures of prior senders and their realizations. I develop a geometric method, recursive concavification, to characterize the Perfect Bayesian Equilibrium paths. I prove the existence of the silent equilibrium, where at most one sender provides nontrivial information. I also show that when there are only two senders and the receiver has a finite action space, it is generically without loss to focus on silent equilibrium. Finally, I show that if there are two senders who have zero-sum payoffs, the truth-telling signal structure is always supported in equilibrium.