Revenue Maximization Mechanisms for an Uninformed Mediator with Communication Abilities

Consider a market where a seller owns an item for sale and a buyer wants to buy an item, and both players have a private type. We study the problem of designing revenue-maximizing mechanisms for a mediator who has no private information but can privately communicate with players. We show that the mediator can, without loss of generality, focus on the set of direct and incentive-compatible mechanisms. Then we formulate this problem as a mathematical program. Moreover, we give an optimal solution to the optimization problem in closed form under certain technical conditions.