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

Abstract

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.

Keywords::

• non-zero-sum stochastic differential games
• Nash equilibrium point
• backward stochastic differential equations

AMS Subject Classification::

• 49N70
• 49N90
• 91A15

Acknowledgement

We are grateful to the two anonymous referees for useful comments and suggestions.

Notes

^1. Email: [email protected]