Optimal Disclosure of Information to a Privately Informed Receiver

Abstract

We study information design problems where the designer controls information about a state and the receiver is privately informed about his preferences. The receiver's action set is general and his preferences depend linearly on the state. We show that to optimally screen the receiver, the designer can use a menu of laminar partitional signals. These signals partition the states such that the same message is sent in each partition element and the convex hulls of any two partition elements are either nested or have an empty intersection. Furthermore, each state is either perfectly revealed or lies in an interval in which at most n+2 different messages are sent, where n is the number of receiver types. In the finite action case an optimal menu can be obtained by solving a finite-dimensional convex program. Along the way we shed light on the solutions of optimization problems over distributions subject to a mean-preserving contraction constraint and additional constraints which might be of independent interest.