The value of mediated communication

This paper characterizes optimal mediation in sender-receiver games. We assume that the mediator's objective is to maximize the ex-ante welfare of the sender. Mediated equilibria are defined by a set of linear incentive constraints. The Lagrange multipliers associated with these constraints yield shadow prices that are used to construct “virtual utility functions” that intuitively characterize the signaling costs of incentive compatibility. Importantly, we characterize the value of an optimal mediation plan (value of mediation) through the concavification of the sender's indirect virtual utility function over posterior beliefs. This result provides necessary and sufficient conditions under which a candidate mediation plan is optimal. An additional result establishes a bound on the number of messages that the sender must convey to achieve the value of mediation.