Multi-Sender Bayesian Persuasion with Imperfect Information

2026-07-09

AI Summary

This study addresses a Bayesian persuasion problem in which multiple senders, each possessing only partial private information about a joint state, aim to influence the decision of a single receiver through strategic signaling. The analysis examines equilibrium structures under the assumption that the receiver can commit to either direct or general randomized action policies, drawing on tools from Bayesian games, information design, and mechanism design. The central contribution is the proof that, provided the receiver has commitment power, there always exists a fully revealing equilibrium—regardless of the prior distribution—in which all senders truthfully report their private information, thereby enabling the receiver to achieve her optimal payoff.

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.

Problem

• Bayesian persuasion
• multi-sender
• imperfect information
• fully informative equilibrium
• signaling

Innovation

• Bayesian persuasion
• multi-sender signaling
• commitment power
• fully informative equilibrium
• strategic information revelation