# A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value

arXiv: https://arxiv.org/abs/1301.4540 · HTML: https://mlsanity.com/paper/1301.4540/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2013.

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

- [Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain](https://mlsanity.com/paper/2509.14203/) (2025)
- [Time-Dependent Blackwell Approachability and Application to Absorbing Games](https://mlsanity.com/paper/2303.04956/) (2023)

## Abstract (arXiv)

We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and the value of the n-stage game does not converge as n goes to infinity.