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

arXiv: https://arxiv.org/abs/1603.02454 · HTML: https://mlsanity.com/paper/1603.02454/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2016.

## Built on by (most cited first, 1 of 1)

- [Risk Sensitivity in Markov Games and Multi-Agent Reinforcement Learning: A Systematic Review](https://mlsanity.com/paper/2406.06041/) (2024)

## Abstract (arXiv)

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.