Nash Equilibrium Approximation under Communication and Computation Constraints in Large-Scale Non-cooperative Games

This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility function of each agent depends on its action, the average of other agents' actions (called the mean variable of that agent) and a deterministic parameter. It is shown that the equilibrium mean variables of all agents converge uniformly to a constant, called asymptotic equilibrium mean (AEM), as the number of agents tends to infinity. The AEM, which depends on the limit of empirical distribution of agents' parameters, determines the asymptotic equilibrium behavior of agents. Next, the problem of approximating the AEM at a processing center under communication and computation constraints is studied. Three approximation methods are proposed to substantially reduce the communication and computation costs of approximating AEM at the processing center. The accuracy of the proposed approximation methods is analyzed and illustrated through numerical examples.