  This work considers stochastic differential games with a large number of
players, whose costs and dynamics interact through the empirical distribution
of both their states and their controls. We develop a new framework to prove
convergence of finite-player games to the asymptotic mean field game. Our
approach is based on the concept of propagation of chaos for forward and
backward weakly interacting particles which we investigate by stochastic
analysis methods, and which appear to be of independent interest. These
propagation of chaos arguments allow to derive moment and concentration bounds
for the convergence of Nash equilibria.
