Informed Principal Problems in Bilateral Trading

We study informed principal problems in a bilateral trade environment in which a seller and a buyer have private information about types affecting their interdependent valuations. Their types might be affiliated and the traders might have different prior beliefs. The informed seller has full bargaining power to design a trading mechanism. We prove the existence of the best separating equilibrium for the seller. The equilibrium outcome is determined by the seller's best incentive-feasible mechanism among those that are ex post incentive compatible and individually rational for the buyer. The best mechanism is characterized as a profile of almost fixed prices. We investigate how the privacy of the seller's information affects the allocative and distributional consequences. Our results are applied to post-auction resale with two asymmetric bidders. We show that the privacy of winners' information about their types raises equilibrium bids but reduces welfare for almost every types