Existence of Nash Equilibrium Points for Markovian Nonzero-sum Stochastic Differential Games with Unbounded Coefficients

TL;DR

This paper proves the existence of Nash equilibrium points in Markovian nonzero-sum stochastic differential games with unbounded coefficients, using multidimensional backward stochastic differential equations.

Contribution

It extends the existence results to cases with unbounded drifts satisfying linear growth, employing multidimensional BSDEs with stochastic linear growth.

Findings

Existence of Nash equilibrium under unbounded drift conditions

Use of multidimensional BSDEs with continuous coefficients

Applicable to Markovian nonzero-sum stochastic differential games

Abstract

This paper is related to nonzero-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.