Social Welfare Maximization and Conformism via Information Design in Linear-Quadratic-Gaussian Games

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.

Average submodularity of maximizing anticoordination in network games

“…That is, we ask if selfish agents can successfully use local interaction to reach maximum polarization in strategies, and if not, can we identify a set of agents whose actions when controlled would lead to the same global objective? Other forms of intervention mechanisms involve financial incentives in the form of taxations or rewards [20], and information design [21], [22]. These mechanisms do not consider repeated game play, and instead focus on improving the efficiency of Nash equilibria.…”

Controlling Networks of Imitative Agents

“…A stochastic framework was introduced in [31], where the effectiveness of a feedback control was investigated by modeling the controlled network as a Markov process. Another line of research has focused on the use of a recommender system that broadcasts to all agents, some carefully constructed non-binding advice [32], [33], [34], including the possibility of a misleading and incorrect advice [35]. There are two key properties that facilitate the design of control algorithms for each of these cases; if the network is at some equilibrium, then providing incentives to the agents should (i) cause no agent to switch away from a desired strategy, and (ii) result in convergence of the network to a unique equilibrium state.…”