Bayesian Persuasion Mediating Cheap Talk

Abstract

We study a multi-player model of sequential communication. A receiver obtains information from two sources. The first is cheap talk with a sender, who acquires the information, while the second is Bayesian persuasion with a mediator, who modifies the initial information. We prove that Bayesian persuasion does not defy truthful communication in cheap talk, but reduces the ex-ante utility of the sender. However, the fineness of the state-space partition in cheap talk can be altered to mitigate utility losses. We also demonstrate that a signalling rule in the persuasion is defined by whether the revealed partition element triggers an action of the receiver that is unfavourable to the mediator. In addition, we characterise preferences of the mediator regarding a cheap-talk partition formed by the sender. Finally, we illustrate our results drawing on a communication process between tax authorities.