Nonzero-Sum Risk Sensitive Stochastic Games for Continuous Time Markov Chains

TL;DR

This paper investigates nonzero-sum risk-sensitive stochastic games for continuous-time Markov chains, establishing existence of Nash equilibria under discounted and ergodic criteria with specific stability and structural assumptions.

Contribution

It proves the existence of Nash equilibria in Markov and stationary strategies for risk-sensitive stochastic games with continuous-time Markov chains under new conditions.

Findings

Existence of solutions to coupled HJB equations for discounted costs.

Nash equilibrium in Markov strategies under additive structure.

Nash equilibrium in stationary strategies under stability and small cost conditions.

Abstract

We study nonzero-sum stochastic games for continuous time Markov chains on a denumerable state space with risk sensitive discounted and ergodic cost criteria. For the discounted cost criterion we first show that the corresponding system of coupled HJB equations has an appropriate solution. Then under an additional additive structure on the transition rate matrix and payoff functions, we establish the existence of a Nash equilibrium in Markov strategies. For the ergodic cost criterion we assume a Lyapunov type stability assumption and a small cost condition. Under these assumptions we show that the corresponding system of coupled HJB equations admits a solution which leads to the existence of Nash equilibrium in stationary strategies.