Coarse Information Design

Abstract

We study an information design problem with continuous state and discrete signal space. We find that the designer's interim value function affects the solution only through its curvature. There is a dual relation between the prior distribution and the marginal value function. Under convex value functions, the optimal information structure is interval-partitional. Moreover, in logconcave environments, a center of scrutiny emerges and information becomes coarser for states farther from it. We locate the scrutiny center and provide comparative statics on information structure with respect to prior distributions and value functions. The analysis can be extended to S-shaped value functions