Nonzero sum stochastic differential games with discounted payoff criterion: An approximating Markov chain approach

We develop a new constructive method for proving the existence of Nash equilibrium for a class of nonzero sum stochastic differential games. Under certain usual assumptions, we prove the existence of Nash equilibrium for discounted payoff criteria. A novel feature of our method is that it allows us to compute Nash equilibrium for a large class of stochastic differential games