Optimal Disclosure of Information to Privately Informed Agents

57 Pages Posted: 11 Mar 2021 Last revised: 11 Feb 2022

See all articles by Ozan Candogan

Ozan Candogan

University of Chicago - Booth School of Business

Philipp Strack

Yale, Department of Economics

Date Written: January 26, 2021

Abstract

We study information design settings where the designer controls information about a state, and there are multiple agents interacting in a game who are privately informed about their types. Each agent’s utility depends on all agents’ types and actions, as well as (linearly) on the state. To optimally screen the agents, the designer first asks agents to report their types and then sends a private action recommendation to each agent whose distribution depends on all reported types and the state. We show that there always exists an optimal mechanism which is laminar partitional. Such a mechanism partitions the state space for each type profile and recommends the same action profile for states that belong to the same partition element. Furthermore, the convex hulls of any two partition elements are such that either one contains the other or they have an empty intersection. In the single-agent case, each state is either perfectly revealed or lies in an interval in which the number of different signal realizations is at most the number of different types of the agent plus two. A similar result is established for the multi-agent case.

We also highlight the value of screening: without screening the best achievable payoff could be as low as one over the number of types fraction of the optimal payoff. 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

Suggested Citation

Candogan, Ozan and Strack, Philipp, Optimal Disclosure of Information to Privately Informed Agents (January 26, 2021). Available at SSRN: https://ssrn.com/abstract=3773326 or http://dx.doi.org/10.2139/ssrn.3773326

Ozan Candogan (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://faculty.chicagobooth.edu/ozan.candogan/

Philipp Strack

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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