Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic Cost Criterion

TL;DR

This paper investigates nonzero-sum stochastic games with risk-sensitive ergodic costs for Markov chains, proving existence and uniqueness of solutions and Nash equilibria under certain conditions.

Contribution

It establishes the existence and uniqueness of solutions to ergodic optimality equations and proves the existence of Nash equilibria in risk-sensitive stochastic games.

Findings

Unique solutions to ergodic optimality equations

Existence of Nash equilibria in stationary strategies

Applicable to controlled Markov chains on Polish spaces

Abstract

In this paper we study infinite horizon nonzero-sum stochastic games for controlled discrete-time Markov chains on a Polish state space with risk-sensitive ergodic cost criterion. Under suitable assumptions we show that the associated ergodic optimality equations admit unique solutions. Finally, the existence of Nash-equilibrium in randomized stationary strategies is established by showing that an appropriate set-valued map has a fixed point.