Robust Verification of Concurrent Stochastic Games

2026-01-17

AI Summary

This work addresses the challenge that transition probabilities in real-world environments often exhibit epistemic uncertainty, rendering existing concurrent stochastic games— which require precise probabilities— ill-suited for practical application. To bridge this gap, we propose robust concurrent stochastic games and their subclass, interval concurrent stochastic games, which, for the first time, support modeling of probabilistic uncertainty. Our framework enables robust verification of both finite- and infinite-horizon objectives under worst-case assumptions, encompassing both zero-sum and non-zero-sum settings. We establish the theoretical foundations of this model, devise efficient verification algorithms, and extend robust analysis to social welfare–optimal Nash equilibria in non-zero-sum games. A prototype implementation in PRISM-games integrates interval probabilities, worst-case reasoning, and symbolic model checking. Experiments on multiple large-scale benchmarks demonstrate the scalability and effectiveness of our approach.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Multiagent Systems under Uncertainty
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

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.

Problem

• concurrent stochastic games
• epistemic uncertainty
• robust verification
• transition probabilities
• multi-agent systems

Innovation

• robust concurrent stochastic games
• interval CSGs
• epistemic uncertainty
• Nash equilibria
• model checking