Optimal Disclosure of Information to a Privately Informed Receiver
46 Pages Posted: 11 Mar 2021 Last revised: 5 Apr 2021
Date Written: January 26, 2021
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 and send the same non-random message in each partition element. The convex hulls of any two partition elements are such that either one contains the other or they 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 side constraints, which might be of independent interest.
Keywords: Information design, private information, laminar partitions
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