Nonzero-sum risk-sensitive stochastic differential games

TL;DR

This paper investigates nonzero-sum stochastic differential games with risk-sensitive criteria, establishing Nash equilibria in Markov and stationary strategies through coupled HJB equations.

Contribution

It introduces a framework for finding Nash equilibria in risk-sensitive nonzero-sum stochastic differential games using coupled HJB equations.

Findings

Existence of Nash equilibrium in Markov strategies for discounted costs

Existence of Nash equilibrium in stationary strategies for ergodic costs

Application of coupled HJB equations to characterize equilibria

Abstract

We study two person nonzero-sum stochastic differential games with risk-sensitive discounted and ergodic cost criteria. Under certain conditions we establish a Nash equilibrium in Markov strategies for the discounted cost criterion and a Nash equilibrium in stationary strategies for the ergodic cost criterion. We achieve our results by studying the relevant systems of coupled HJB equations.