# On Completely Mixed Stochastic Games

arXiv: https://arxiv.org/abs/1703.04619 · HTML: https://mlsanity.com/paper/1703.04619/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [Regularized Gradient Descent Ascent for Two-Player Zero-Sum Markov Games](https://mlsanity.com/paper/2205.13746/) (2022)

## Abstract (arXiv)

In this paper, we consider a zero-sum undiscounted stochastic game which has finite state space and finitely many pure actions. Also, we assume the transition probability of the undiscounted stochastic game is controlled by one player and all the optimal strategies of the game are strictly positive. Under all the above assumptions, we show that the β-discounted stochastic games with the same payoff matrices and β sufficiently close to 1 are also completely mixed. We give a counterexample to show that the converse of the above result in not true. We also show that, if we have non-zero value in some state for the undiscounted stochastic game then for β sufficiently close to 1 the β-discounted stochastic game also possess nonzero value in the same state.