Discrete-time average-cost mean-field games on Polish spaces

Abstract

In stochastic dynamic games, when the number of players is sufficiently large and the interactions betweenagents depend on empirical state distribution, one way to approximate the original game is to introduce infinitepopulation limit of the problem. In the infinite population limit, a generic agent is faced with a so-called mean-fieldgame. In this paper, we study discrete-time mean-field games with average-cost criteria. Using average cost optimalityequation and Kakutani’s fixed point theorem, we establish the existence of Nash equilibria for mean-field games underdrift and minorization conditions on the dynamics of each agent. Then, we show that the equilibrium policy in themean-field game, when adopted by each agent, is an approximate Nash equilibrium for the corresponding finite-agentgame with sufficiently many agents.