Coarse Information Design

TL;DR

This paper investigates optimal information structures with continuous states and discrete signals, revealing an interval-partitional form with dual expectation properties under convex and S-shaped value functions.

Contribution

It characterizes the structure of optimal information design and extends the analysis to general value functions and coarse mechanism design.

Findings

Optimal structure is interval-partitional with dual expectation properties.

The analysis applies to general value functions.

Insights into which state space parts are more finely partitioned.

Abstract

We study an information design problem with continuous state and discrete signal space. Under convex and S-shaped value functions, the optimal information structure is interval-partitional and exhibits a dual expectations property: each induced signal is the conditional mean (taken under the prior density) of each interval; and each interval cutoff is the barycenter (taken under the value function curvature) of the interval formed by neighboring signals. This property enables an examination into which part of the state space is more finely partitioned. The analysis can be extended to general value functions and adapted to study coarse mechanism design.