Discrete-Time Ergodic Mean-Field Games with Average Reward on Compact Spaces

We present a model of discrete-time mean-field game with compact state and action spaces and average reward. Under some strong ergodicity assumption, we show it possesses a stationary mean-field equilibrium. We present an example showing that in general an equilibrium for this game may not be a good approximation of Nash equilibria of the n-person stochastic game counterparts of the mean-field game for large n. Finally, we identify two cases when the approximation is good.