# Symbolic Verification and Strategy Synthesis for Turn-based Stochastic Games

arXiv: https://arxiv.org/abs/2211.06141 · HTML: https://mlsanity.com/paper/2211.06141/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2022.

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

- [Turn-based Multi-Agent Reinforcement Learning Model Checking](https://mlsanity.com/paper/2501.03187/) (2025)
- [Multi-Agent Verification and Control with Probabilistic Model Checking](https://mlsanity.com/paper/2308.02829/) (2023)
- [Social Laws for Multi-agent Coordination in Stochastic Environments](https://mlsanity.com/paper/2609.18929/) (2026)

## Abstract (arXiv)

Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally specify quantitative specifications of either collective or individual behaviour and then automatically synthesise strategies for the agents under which these specifications are guaranteed to be satisfied. Although good progress has been made on algorithms and tool support, efficiency and scalability remain a challenge. In this paper, we investigate a symbolic implementation based on multi-terminal binary decision diagrams. We describe how to build and verify turn-based stochastic games against either zero-sum or Nash equilibrium based temporal logic specifications. We collate a set of benchmarks for this class of games, and evaluate the performance of our approach, showing that it is superior in a number of cases and that strategies synthesised in a symbolic fashion can be considerably more compact.