Rational Capability in Concurrent Games

2025-02-17

AI Summary

This paper addresses the formalization challenge of coalition rationality in concurrent multi-agent games. It introduces a minimal rational preference model based on dominance relations and provides the first rigorous definition of “rational enforceability”—the ability of a rational coalition to guarantee a temporal property under preference constraints—within concurrent game structures (CGS). Methodologically, it extends classical Coalition Logic (CL) and Alternating-Time Temporal Logic (ATL) with rational capability modalities, establishes their minimal rational semantics, and determines the exact computational complexity of satisfiability and model checking: PSPACE-complete for the CL variant and EXPTIME-complete for the ATL variant. Key contributions include: (1) the first logical framework formally capturing rational capability; (2) a decidable semantics accompanied by a sound and complete axiomatization; and (3) a theoretical foundation and precise computational boundaries for verifying rational multi-agent behavior.

Technology Category

Knowledge Representation and Reasoning: PreferencesMultiagent Systems: Mechanism DesignGame Theory and Economic Paradigms: Cooperative Game Theory

Application Category

Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactionsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsResponsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We extend concurrent game structures (CGSs) with a simple notion of preference over computations and define a minimal notion of rationality for agents based on the concept of dominance. We use this notion to interpret a CL and an ATL languages that extend the basic CL and ATL languages with modalities for rational capability, namely, a coalition's capability to rationally enforce a given property. For each of these languages, we provide results about the complexity of satisfiability checking and model checking as well as about axiomatization.

Problem

• Extend concurrent game structures with preference.
• Define minimal rationality based on dominance.
• Analyze complexity of satisfiability and model checking.

Innovation

• Extend CGSs with preference
• Define minimal rationality concept
• Provide complexity and axiomatization results