LQG Information Design

Abstract: This paper addresses information design in a workhorse model of network games, where agents have linear best responses, the information designer optimizes a quadratic objective, and the payoff state follows a multivariate Gaussian distribution. We formulate the problem as semidefinite programming (SDP) and utilize the duality principle to characterize an optimal information structure. A Gaussian information structure is shown to be optimal among all information structures. A necessary and sufficient condition for optimality is that the induced equilibrium strategy profile and the state jointly satisfy a linear constraint derived from complementary slackness conditions. Consequently, the true state is typically revealed to the entire population of agents, even though individual agents remain only partially informed. In symmetric network games, an optimal information structure inherits the same degree of symmetry, which facilitates its computation.