Existence of Nash equilibrium points for Markovian non-zero-sum stochastic differential games with unbounded coefficients

This paper is related to non-zero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with continuous coefficient and stochastic linear growth.