  A linear-quadratic-Gaussian (LQG) game is an incomplete information game with
quadratic payoff functions and Gaussian payoff states. This study addresses an
information design problem to identify an information structure that maximizes
a quadratic objective function. Gaussian information structures are found to be
optimal among all information structures. Furthermore, the optimal Gaussian
information structure can be determined by semidefinite programming, which is a
natural extension of linear programming. This paper provides sufficient
conditions for the optimality and suboptimality of both no and full information
disclosure. In addition, we characterize optimal information structures in
symmetric LQG games and optimal public information structures in asymmetric LQG
games, with each structure presented in a closed-form expression.

Theoretical Economics;Systems and Control;Systems and Control