Linear Quadratic Mean-Field Games with Communication Constraints

TL;DR

This paper develops a mean-field game framework for large populations with heterogeneous agents facing communication constraints, providing a scalable way to compute equilibrium controls and demonstrating their effectiveness through simulations.

Contribution

It introduces a novel approach to solve large-scale mean-field games with communication constraints, deriving explicit linear equilibrium policies and proving their near-optimality in finite populations.

Findings

Equilibrium control policies are independent of dual effects.

Mean-field trajectories follow linear dynamics.

Finite population controls form an epsilon-Nash equilibrium.

Abstract

In this paper, we study a large population game with heterogeneous dynamics and cost functions solving a consensus problem. Moreover, the agents have communication constraints which appear as: (1) an Additive-White Gaussian Noise (AWGN) channel, and (2) asynchronous data transmission via a fixed scheduling policy. Since the complexity of solving the game increases with the number of agents, we use the Mean-Field Game paradigm to solve it. Under standard assumptions on the information structure of the agents, we prove that the control of the agent in the MFG setting is free of the dual effect. This allows us to obtain an equilibrium control policy for the generic agent, which is a function of only the local observation of the agent. Furthermore, the equilibrium mean-field trajectory is shown to follow linear dynamics, hence making it computable. We show that in the finite population game, the equilibrium control policy prescribed by the MFG analysis constitutes an $\epsilon$-Nash equilibrium, where $\epsilon$ tends to zero as the number of agents goes to infinity. The paper is concluded with simulations demonstrating the performance of the equilibrium control policy.