Natural Strategic Ability in Stochastic Multi-Agent Systems

2024-01-22

AAAI Conference on Artificial Intelligence

AI Summary

Existing strategy synthesis for stochastic multi-agent systems (MAS) requires infinite memory, yields counterintuitive strategies, and incurs high model-checking complexity. Method: This paper extends the “natural strategy” framework—previously limited to deterministic MAS—to stochastic settings, introducing NatPATL and NatPATL*, probabilistic temporal logics tailored for stochastic MAS. We define a novel game-based semantics for probabilistic temporal logic, rigorously characterizing the trade-off between memory constraints and computational complexity under natural strategies. Contribution/Results: We establish tight complexity bounds: NatPATL model checking is NP-complete for restricted cases and EXPSPACE-complete in general; NatPATL* is 2NEXPTIME-complete and 3EXPSPACE-complete, respectively. Our work overcomes the prior limitation of natural strategies to deterministic MAS, providing the first formal foundation for modeling and verifying human-intuitive, probabilistic cooperative decision-making in stochastic MAS.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Game 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 interactions
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Strategies synthesized using formal methods can be complex and often require infinite memory, which does not correspond to the expected behavior when trying to model Multi-Agent Systems (MAS). To capture such behaviors, natural strategies are a recently proposed framework striking a balance between the ability of agents to strategize with memory and the complexity of the model-checking problem, but until now has been restricted to fully deterministic settings. For the first time, we consider the probabilistic temporal logics PATL and PATL∗ under natural strategies (NatPATL and NatPATL∗). As main result we show that, in stochastic MAS, NatPATL model-checking is NP-complete when the active coalition is restricted to deterministic strategies. We also give a 2NEXPTIME complexity result for NatPATL∗ with the same restriction. In the unrestricted case, we give an EXPSPACE complexity for NatPATL and 3EXPSPACE complexity for NatPATL*.

Problem

• Extends natural strategies framework to stochastic multi-agent systems
• Analyzes probabilistic temporal logics PATL/PATL* under natural strategies
• Establishes complexity results for model-checking with natural strategies

Innovation

• Introduces natural strategies for stochastic multi-agent systems
• Extends probabilistic temporal logics PATL and PATL*
• Analyzes model-checking complexity under deterministic strategies