Lemonade from Lemons: Information Design and Adverse Selection

Navin Kartik (Columbia University)

Paper Abstract (with Weijie Zhong):

A buyer makes a take-it-or-leave-it offer to a seller for a single object. The two parties’ values may be interdependent. We study the set of payoff vectors that can be implemented (in sequential equilibria) using joint information design. We establish, in part constructively, that the set is a triangle characterized by simple feasibility and individual-rationality constraints. We also investigate what is implementable only using information structures in which the seller is more informed than the buyer, or more generally, under a “no signaling” equilibrium restriction. We show that there is then no loss in providing the buyer with no information and only varying the seller’s information; i.e., familiar adverse-selection structures emerge. However, except in some notable special cases, these information structures do not implement all payoff vectors—in particular, they do not maximize the seller’s payoff or minimize the buyer’s payoff. Our model encompasses monopoly pricing, for which our results augment those of Bergemann, Brooks, and Morris (2015) and Roesler and Szentes (2017).