Strategic Coalitions in Stochastic Games
This work addresses formal verification and strategic reasoning in multi-agent systems, particularly for safety-critical applications, but it is incremental as it builds on existing stochastic game and modal logic frameworks.
The paper tackles the problem of modeling strategic coalitions in stochastic games with failure states by introducing two logical systems that describe coalition strategies for avoiding failure and achieving goals with specified probabilities. The main results include completeness theorems for one system and an incompleteness theorem showing no strongly complete system exists when including the empty coalition.
The article introduces a notion of a stochastic game with failure states and proposes two logical systems with modality "coalition has a strategy to transition to a non-failure state with a given probability while achieving a given goal." The logical properties of this modality depend on whether the modal language allows the empty coalition. The main technical results are a completeness theorem for a logical system with the empty coalition, a strong completeness theorem for the logical system without the empty coalition, and an incompleteness theorem which shows that there is no strongly complete logical system in the language with the empty coalition.