2017/04/19 by Ehsan Nekouei, Nekouei, Ehsan, Tansu Alpcan +3
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Mathematics #Game Theory and Applications #Merger and Competition Analysis #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1704.05653
openalex publication_date 2017/04/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
This paper studies the problem of Nash equilibrium approximation in\nlarge-scale heterogeneous mean-field games under communication and computation\nconstraints. A deterministic mean-field game is considered in which the\nnon-linear utility function of each agent depends on its action, the average of\nother agents' actions (called the mean variable of that agent) and a\ndeterministic parameter. It is shown that the equilibrium mean variables of all\nagents converge uniformly to a constant, called asymptotic equilibrium mean\n(AEM), as the number of agents tends to infinity. The AEM, which depends on the\nlimit of empirical distribution of agents' parameters, determines the\nasymptotic equilibrium behavior of agents. Next, the problem of approximating\nthe AEM at a processing center under communication and computation constraints\nis studied. Three approximation methods are proposed to substantially reduce\nthe communication and computation costs of approximating AEM at the processing\ncenter. The accuracy of the proposed approximation methods is analyzed and\nillustrated through numerical examples.\n