Maximizing Social Welfare and Agreement via Information Design in Linear-Quadratic-Gaussian Games

TL;DR

This paper analyzes how an information designer can optimize social welfare and agreement among players in linear-quadratic-Gaussian games by controlling information disclosure, deriving analytical solutions and exploring strategic effects.

Contribution

It provides analytical solutions for optimal information disclosure in LQG games and explores conditions under which full or partial disclosure maximizes social welfare or agreement.

Findings

Full information disclosure maximizes social welfare with common payoff states or public signals.

Hiding information is optimal for inducing conformity among players.

The value of information disclosure increases with strategic substitution.

Abstract

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.