Strategic Coalitions in Stochastic Games

TL;DR

This paper develops logical frameworks for stochastic games with failure states, analyzing coalition strategies with probabilistic goals, and establishes key completeness and incompleteness results for these logical systems.

Contribution

It introduces new logical systems for stochastic games with failure states and proves their completeness properties, advancing formal reasoning about probabilistic coalition strategies.

Findings

Completeness theorem for logical system with empty coalition

Strong completeness theorem for logical system without empty coalition

Incompleteness result for the language with empty coalition

Abstract

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.