The Bounds of Mediated Communication

Abstract

We study the bounds of mediated communication in sender-receiver games in which the sender's payoff is state-independent. We show that the feasible distributions of beliefs under mediation are those that induce zero correlation, but not necessarily independence, between the sender's payoff and the receiver's belief. Mediation attains the upper bound on the sender's value, i.e., the Bayesian persuasion value, if and only if this value collapses to the lower bound, i.e., the cheap talk value. Mediation is strictly above this lower bound when the sender has countervailing incentives in the space of the receiver's belief, as captured by a failure of a weak single-crossing condition. We apply our results to asymmetric-information settings such as bilateral trade and lobbying and explicitly construct mediation policies such that the informed and uninformed parties are better off than under unmediated communication. (with Yifan Dai)