Social Welfare Maximization and Conformism via Information Design in Linear-Quadratic-Gaussian Games Furkan Sezer, Hossein Khazaei, and Ceyhun Eksin * February 26, 2021 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. 1 Introduction In an incomplete information game, multiple players compete to maximize their individual payoffs that depend on the action of the player, other players’ actions and on the realization of an unknown state. Incomplete information games are used to model power allocation of users in wireless networks with unknown channel gains [1, 2, 3, 4], traffic flow in communication or transportation networks [5, 6, 7], oligopoly price competition [8, 9], consumer behavior in a demand response management scheme [10, 11], coordination of autonomous teams [12, 13], and currency attacks of investors [14, 15]. The information design problem refers to the determination of the information fidelity of the signals given to the players so that the induced actions of players maximize a system level objective. In this problem, we can envision the existence of an information designer that can provide the “best” information about the payoff-relevant unknown states to the players according to its objective. As per the above examples, the information designer can represent an entity such as a system designer overseeing the spectrum allocation, a market-maker, an independent * Authors are with the Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843 USA (e-mails: furkan.sezer@tamu.edu, h.khazaei@tamu.edu, eksinc@tamu.edu). This work was supported by NSF CCF- 2008855. 1 arXiv:2102.13047v1 [math.OC] 25 Feb 2021