Saldı, NaciBaşar, T.Raginsky, M.2020-05-152020-05-1520180363-0129http://hdl.handle.net/10679/6571https://doi.org/10.1137/17M1112583In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number $N$ of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov--Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptions, we demonstrate the existence of a mean-field equilibrium in the infinite-population limit $N \to \infty$, and then show that the policy obtained from the mean-field equilibrium is approximately Markov--Nash when the number of agents $N$ is sufficiently large.engrestrictedAccessMarkov-Nash equilibria in mean-field games with discounted costarticle5664256428700045378590001410.1137/17M1112583Mean-field gamesNash equilibriumDiscounted cost2-s2.0-85060054062