Information Design in Smooth Games

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.