Lemonade from lemons: Information design and adverse selection

A seller posts a price for a single object. The seller's and buyer's values may be interdependent. We characterize the set of payoff vectors across all information structures. Simple feasibility and individual-rationality constraints identify the payoff set. The buyer can obtain the entire surplus; often, noninformational mechanisms cannot enlarge the payoff set. We also study payoffs when the buyer is more informed than the seller, and when the buyer is fully informed. All three payoff sets coincide (only) in notable special cases—in particular, when there is complete breakdown in a “lemons market” with an uninformed seller and fully informed buyer.