The Bounds of Mediated Communication

We study sender-receiver games with transparent motives, where an uninformed, sender-aligned mediator commits to a communication mechanism but cannot verify the sender's report. We compare mediated communication with cheap talk and Bayesian persuasion. A belief-value distribution is implementable by mediation exactly when it satisfies Bayes plausibility, receiver obedience, and zero covariance between posterior beliefs and sender values. This formulation separates the roles of commitment and verifiability. We show that mediation attains the persuasion value only when cheap talk also does; thus, whenever persuasion strictly outperforms cheap talk, unverifiable reports create a strict loss. We characterize when mediation strictly improves on cheap talk: the sender's value must exhibit countervailing effects along some direction in belief space. In finite-action, binary-state environments, this characterization yields a tractable description of optimal mediation. Applications cover platforms, lobbying, acceptance games, and a reinterpretation of the model as matching with externalities, where we study the efficiency-fairness tradeoff.