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

arXiv: https://arxiv.org/abs/1603.03683 · HTML: https://mlsanity.com/paper/1603.03683/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 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)

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.