Multi-Sender Bayesian Persuasion with Imperfect Information

Abstract

We study a multi-sender Bayesian persuasion problem with one receiver and several strategic senders. The underlying ground state has multiple components, each privately observed by a different sender, while the receiver holds a common prior over the joint state space. Senders simultaneously choose signaling policies, and the receiver takes an action based on the posterior induced by the signals; each is sampled independently from the sender's signaling policy. We analyze the game induced by the receiver's straightforward policy, which selects a receiver-optimal action at every posterior. In particular, we characterize the senders' best responses under the straightforward policy and identify conditions on the prior that induce a fully informative equilibrium; i.e., truthfully reporting the ground truth is an equilibrium strategy for every sender. These conditions capture cases in which senders' incentives are sufficiently aligned to enable full revelation without additional commitment from the receiver. The important contribution of this paper is to analyze games induced by a more general (possibly randomized) class of action policies that the receiver commits to before senders choose their signaling strategies. We show that this commitment power fundamentally changes the problem. In particular, we show that for any prior over the joint state space, the receiver can construct action policies that maximize her payoff while ensuring a fully informative equilibrium.