Information Design in Smooth Games

TL;DR

This paper characterizes optimal information structures in smooth games with continuous actions, showing their connection to principal-agent problems and providing explicit solutions for specific game classes.

Contribution

It establishes a link between optimal information design and principal-agent implementation, and characterizes optimal disclosures in linear-quadratic games.

Findings

Targeted disclosure is robustly optimal with common values.

Linear disclosure is uniquely optimal with interdependent, normally distributed values.

Applications include venture capital, Bayesian polarization, and price competition.

Abstract

We study information design in games where players choose from a continuum of actions and have continuously differentiable payoffs. We show that an information structure is optimal when the equilibrium it induces can also be implemented in a principal-agent contracting problem. Building on this result, we characterize optimal information structures in symmetric linear-quadratic games. With common values, targeted disclosure is robustly optimal across all priors. With interdependent and normally distributed values, linear disclosure is uniquely optimal. We illustrate our findings with applications in venture capital, Bayesian polarization, and price competition.