Zero-sum Risk-sensitive Stochastic Games for Continuous Time Markov Chains

TL;DR

This paper investigates zero-sum stochastic games with risk-sensitive criteria for continuous-time Markov chains, establishing the existence of equilibrium strategies and values for both discounted and ergodic costs under certain conditions.

Contribution

It proves the existence of saddle-point equilibria and game values for risk-sensitive stochastic games on continuous-time Markov chains, extending prior results to more general settings.

Findings

Existence of value and saddle-point equilibrium for discounted-cost games.

Existence of value and saddle-point equilibrium for ergodic-cost games.

Application of Hamilton-Jacobi-Isaacs equation under Lyapunov conditions.

Abstract

We study infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled continuous time Markov chains on a countable state space. For the discounted-cost game we prove the existence of value and saddle-point equilibrium in the class of Markov strategies under nominal conditions. For the ergodic-cost game we prove the existence of values and saddle point equilibrium by studying the corresponding Hamilton-Jacobi-Isaacs equation under a certain Lyapunov condition.