# Discrete-time Zero-Sum Games for Markov chains with risk-sensitive average cost criterion

arXiv: https://arxiv.org/abs/2201.03790 · HTML: https://mlsanity.com/paper/2201.03790/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2022.

## Built on by (most cited first, 2 of 2)

- [Risk-Sensitive Multi-Agent Reinforcement Learning in Network Aggregative Markov Games](https://mlsanity.com/paper/2402.05906/) (2024)
- [Risk Sensitivity in Markov Games and Multi-Agent Reinforcement Learning: A Systematic Review](https://mlsanity.com/paper/2406.06041/) (2024)

## Abstract (arXiv)

We study zero-sum stochastic games for controlled discrete time Markov chains with risk-sensitive average cost criterion with countable state space and Borel action spaces. The payoff function is nonnegative and possibly unbounded. Under a certain Lyapunov stability assumption on the dynamics, we establish the existence of a value and saddle point equilibrium. Further we completely characterize all possible saddle point strategies in the class of stationary Markov strategies. Finally, we present and analyze an illustrative example.