Information Design Possibility Set

TL;DR

This paper characterizes the set of all achievable expected value combinations in information design, demonstrating its convexity and continuity properties, which facilitate new optimization methods and broaden problem tractability.

Contribution

It establishes the convexity and continuity of the information design possibility set, enabling a concavification approach for constrained optimization in information design.

Findings

The set of all expected value combinations is compact and convex.

The correspondence of the set with respect to prior is continuous.

Provides a new method for solving constrained optimization problems in information design.

Abstract

Let $\mathcal{V}$ be the set of all combinations of expected value of finite objective functions from designing information. I showed that $\mathcal{V}$ is a compact and convex set implemented by signal structures with finite support when unknown states are finite. Moreover, $\mathcal{V}(\mu)$ as a correspondence of prior is continuous. This result can be applied to develop a concavification method of Lagrange multipliers that works with general constrained optimization. It also provides tractability to a wide range of information design problems.