Anahtarcı, BKarıksız, C. D.Saldı, NaciAlekh Agarwal2024-03-142024-03-142023-12-161532-4435https://hdl.handle.net/11693/114716We consider learning approximate Nash equilibria for discrete-time mean-field games with stochastic nonlinear state dynamics subject to both average and discounted costs. To this end, we introduce a mean-field equilibrium (MFE) operator, whose fixed point is a mean-field equilibrium, i.e., equilibrium in the infinite population limit. We first prove that this operator is a contraction, and propose a learning algorithm to compute an approximate mean-field equilibrium by approximating the MFE operator with a random one. Moreover, using the contraction property of the MFE operator, we establish the error analysis of the proposed learning algorithm. We then show that the learned mean-field equilibrium constitutes an approximate Nash equilibrium for finite-agent games.enCC BY 4.0Mean- field gamesApproximate Nash equilibriumFitted Q-iteration algo-rithmDiscounted-costAverage-costArticle1533-7928