On the Convergence to a Mean-Field Equilibrium

Mean-field games model strategic decision making of small interacting individuals in an infinite population. We study the convergence of the equilibria of N-player games to mean-field equilibria. We define classes of strategies over which any equilibrium converges to a mean-field equilibrium when the number of players goes to infinity. We also exhibit equilibria outside this class that do not converge to mean-field equilibria. This implies that mean-field games are not the limit of games with very large populations.