Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space

TL;DR

This paper investigates nonzero-sum stochastic games with countable states, establishing the existence of Nash equilibria in Markov and stationary Markov strategies for both discounted and ergodic costs under certain conditions.

Contribution

It proves the existence of Nash equilibrium strategies in Markov and stationary Markov strategies for infinite horizon risk-sensitive stochastic games with countable states.

Findings

Nash equilibria exist for discounted-cost games under general conditions.

Nash equilibria in stationary strategies exist for ergodic-cost games with additional conditions.

Results apply to controlled Markov chains with countably many states.

Abstract

The infinite horizon risk-sensitive discounted-cost and ergodic-cost nonzero-sum stochastic games for controlled Markov chains with countably many states are analyzed. For the discounted-cost game, we prove the existence of Nash equilibrium strategies in the class of Markov strategies under fairly general conditions. Under an additional geometric ergodicity condition and a small cost criterion, the existence of Nash equilibrium strategies in the class of stationary Markov strategies is proved for the ergodic-cost game.