# Equilibria-based Probabilistic Model Checking for Concurrent Stochastic Games

arXiv: https://arxiv.org/abs/1811.07145 · HTML: https://mlsanity.com/paper/1811.07145/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2018.

## Built on by (most cited first, 8 of 8)

- [Multi-Agent Reinforcement Learning with Temporal Logic Specifications](https://mlsanity.com/paper/2102.00582/) (2021)
- [Specification-Guided Learning of Nash Equilibria with High Social Welfare](https://mlsanity.com/paper/2206.03348/) (2022)
- [Counterfactual Reasoning for Causal Responsibility Attribution in Probabilistic Multi-Agent Systems](https://mlsanity.com/paper/2605.13077/) (2026)
- [Rational Verification for Probabilistic Systems](https://mlsanity.com/paper/2107.09119/) (2021)
- [Responsibility-aware Strategic Reasoning in Probabilistic Multi-Agent Systems](https://mlsanity.com/paper/2411.00146/) (2024)
- [Robust Verification of Concurrent Stochastic Games](https://mlsanity.com/paper/2601.12003/) (2026)
- [On Quantified Observability Analysis in Multiagent Systems](https://mlsanity.com/paper/2310.02614/) (2023)
- [Probabilistic Strategy Logic with Degrees of Observability](https://mlsanity.com/paper/2412.15135/) (2024)

## Abstract (arXiv)

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus on zero-sum goals and cannot reason about scenarios where entities are endowed with different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to allow reasoning about players with distinct quantitative goals, which capture either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in the PRISM-games tool and apply them to several case studies, including network protocols and robot navigation, showing the benefits compared to existing approaches.