Coordinated Sequential Bayesian Persuasion∗

This paper studies an extended Bayesian Persuasion model in which multiple senders persuade one Receiver sequentially and the subsequent players can always observe previous signaling rules and their realizations. In the spirit of Harris (1985), I develop the recursive concavification method to characterize the Subgame Perfect Equilibrium, which summarizes the multiplicity of possible strategic interactions among senders and identifies the ranges of their equilibrium payoffs. Furthermore, I prove the existence of a special type of equilibrium, called the Silent Equilibrium, where at most one sender designs a nontrivial signaling rule. Also, I show that in zero-sum games, the truth-telling information structure is always supported in equilibrium. Finally, I make comparisons with a simultaneous multi-sender Bayesian persuasion model (Gentzkow and Kamenica 2017b) and examine the impact of the order of persuasion. A geometric version of Blackwell’s order is adopted for examination of informativeness.