On the bang-bang type Nash equilibrium point for Markovian nonzero-sum stochastic differential game

TL;DR

This paper investigates the existence of bang-bang type Nash equilibria in Markovian nonzero-sum stochastic differential games, utilizing multidimensional backward stochastic differential equations with discontinuous generators.

Contribution

It establishes the existence of a discontinuous, bang-bang type Nash equilibrium in a Markovian stochastic differential game using backward stochastic differential equations.

Findings

Existence of bang-bang Nash equilibrium under natural conditions

Discontinuous Nash equilibria characterized in the Markovian setting

Application of multidimensional BSDEs with discontinuous generators

Abstract

In this paper, we study a nonzero-sum stochastic differential game in Markovian framework. We show the existence of the Nash equilibrium point which is discontinuous and of bang-bang type under natural conditions. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component.