  We consider linear-quadratic Gaussian (LQG) games in which players have
quadratic payoffs that depend on the players' actions and an unknown
payoff-relevant state, and signals on the state that follow a Gaussian
distribution conditional on the state realization. An information designer
decides the fidelity of information revealed to the players in order to
maximize the social welfare of the players or reduce the disagreement among
players' actions. Leveraging the semi-definiteness of the information design
problem, we derive analytical solutions for these objectives under specific LQG
games. We show that full information disclosure maximizes social welfare when
there is a common payoff-relevant state, when there is strategic
substitutability in the actions of players, or when the signals are public.
Numerical results show that as strategic substitution increases, the value of
the information disclosure increases. When the objective is to induce
conformity among players' actions, hiding information is optimal. Lastly, we
consider the information design objective that is a weighted combination of
social welfare and cohesiveness of players' actions. We obtain an interval for
the weights where full information disclosure is optimal under public signals
for games with strategic substitutability. Numerical solutions show that the
actual interval where full information disclosure is optimal gets close to the
analytical interval obtained as substitution increases.
