Noisy mean field stochastic games with network applications

We consider a class of stochastic games with finite number of resource states, individual states and actions per states. At each stage, a random set of players interact. The states and the actions of all the interacting players determine together the instantaneous payoffs and the transitions to the next states. We study the convergence of the stochastic game with variable set of interacting players when the total number of possible players grow without bound. We show that the optimal payoffs, the mean field equilibrium payoffs are solution of coupled system of backward-forward equations. The limiting games are equivalent to discrete time anonymous sequential games or to differential population games. Using multidimensional diffusion process, a general mean field convergence to stochastic differential equation is given. We illustrate the controlled mean field limit in wireless networks.