Before revision:  We analyse the mean-field game (MFG) limit of the stochastic game and show that the Nash equilibria is given by the solution to a non-standard vector-valued forward-backward stochastic differential equation.
After revision:  We analyse the mean-field game (MFG) limit of the stochastic game and show that the Nash equilibrium is given by the solution to a non-standard vector-valued forward-backward stochastic differential equation.