# Robust Verification of Concurrent Stochastic Games

arXiv: https://arxiv.org/abs/2601.12003 · HTML: https://mlsanity.com/paper/2601.12003/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 52 references that are in the map.
- First posted on arXiv 17 Jan 2026.

## Builds on (most cited first, 12 of 12)

- [Sample-Efficient Robust Multi-Agent Reinforcement Learning in the Face of Environmental Uncertainty](https://mlsanity.com/paper/2404.18909/) (2024)
- [Robust Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2301.00858/) (2023)
- [Solving Robust Markov Decision Processes: Generic, Reliable, Efficient](https://mlsanity.com/paper/2412.10185/) (2024)
- [Solving Long-run Average Reward Robust MDPs via Stochastic Games](https://mlsanity.com/paper/2312.13912/) (2023)
- [Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games](https://mlsanity.com/paper/1811.07145/) (2018)
- [Automatic Verification of Concurrent Stochastic Systems](https://mlsanity.com/paper/2008.04613/) (2020)
- [Imprecise Probabilities Meet Partial Observability: Game Semantics for Robust POMDPs](https://mlsanity.com/paper/2405.04941/) (2024)
- [Correlated Equilibria and Fairness in Concurrent Stochastic Games](https://mlsanity.com/paper/2201.09702/) (2022)
- [Multi-player Equilibria Verification for Concurrent Stochastic Games](https://mlsanity.com/paper/2007.03365/) (2020)
- [Sample-Efficient Distributionally Robust Multi-Agent Reinforcement Learning via Online Interaction](https://mlsanity.com/paper/2508.02948/) (2025)
- [Distributionally Robust Markov Games with Average Reward](https://mlsanity.com/paper/2508.03136/) (2025)
- [Polytopal Stochastic Games](https://mlsanity.com/paper/2502.16208/) (2025)

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

- [Robust PAC Learning of Concurrent Stochastic Games](https://mlsanity.com/paper/2609.04189/) (2026)

## Abstract (arXiv)

Autonomous systems often operate in multi-agent settings and need to make concurrent, strategic decisions, typically in uncertain environments. Verification and control problems for these systems can be tackled with concurrent stochastic games (CSGs), but this model requires transition probabilities to be precisely specified - an unrealistic requirement in many real-world settings. We introduce *robust CSGs* and their subclass *interval CSGs* (ICSGs), which capture epistemic uncertainty about transition probabilities in CSGs. We propose a novel framework for *robust* verification of these models under worst-case assumptions about transition uncertainty. Specifically, we develop the underlying theoretical foundations and efficient algorithms, for finite- and infinite-horizon objectives in both zero-sum and nonzero-sum settings, the latter based on (social-welfare optimal) Nash equilibria. We build an implementation in the PRISM-games model checker and demonstrate the feasibility of robust verification of ICSGs across a selection of large benchmarks.