A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals

TL;DR

This paper introduces a backward stochastic differential equation framework to analyze Nash equilibrium payoffs in nonzero-sum stochastic differential games with nonlinear costs, extending previous theoretical results.

Contribution

It provides existence and characterization theorems for Nash equilibrium payoffs using doubly controlled backward stochastic differential equations, advancing the theoretical understanding of such games.

Findings

Established existence of Nash equilibrium payoffs.

Provided a characterization theorem for these payoffs.

Extended previous results to more general nonlinear cost functionals.

Abstract

In this paper, we study Nash equilibrium payoffs for nonzero-sum stochastic differential games via the theory of backward stochastic differential equations. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined with the help of a doubly controlled backward stochastic differential equation. Our results extend former ones by Buckdahn, Cardaliaguet and Rainer (2004) and are based on a backward stochastic differential equation approach.