# Multi-player Equilibria Verification for Concurrent Stochastic Games

arXiv: https://arxiv.org/abs/2007.03365 · HTML: https://mlsanity.com/paper/2007.03365/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [Rational Verification for Probabilistic Systems](https://mlsanity.com/paper/2107.09119/) (2021)
- [Robust Verification of Concurrent Stochastic Games](https://mlsanity.com/paper/2601.12003/) (2026)
- [Expectation vs. Reality: Towards Verification of Psychological Games](https://mlsanity.com/paper/2411.05599/) (2024)

## Abstract (arXiv)

Concurrent stochastic games (CSGs) are an ideal formalism for modelling probabilistic systems that feature multiple players or components with distinct objectives making concurrent, rational decisions. Examples include communication or security protocols and multi-robot navigation. Verification methods for CSGs exist but are limited to scenarios where agents or players are grouped into two coalitions, with those in the same coalition sharing an identical objective. In this paper, we propose multi-coalitional verification techniques for CSGs. We use subgame-perfect social welfare (or social cost) optimal Nash equilibria, which are strategies where there is no incentive for any coalition to unilaterally change its strategy in any game state, and where the total combined objectives are maximised (or minimised). We present an extension of the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) to specify equilibria-based properties for any number of distinct coalitions, and a corresponding model checking algorithm for a variant of stopping games. We implement our techniques in the PRISM-games tool and apply them to several case studies, including a secret sharing protocol and a public good game.