Modeling Concurrent Multi-Agent Systems

2026-02-09

AI Summary

Existing approaches to modeling concurrent multi-agent systems struggle to balance expressiveness and tractability. This work proposes a novel modeling paradigm based on circuit representations, integrating formal methods, game-theoretic equilibrium concepts, and computational complexity theory to overcome the expressiveness limitations and intractability inherent in explicit models for equilibrium analysis. Within this framework, we provide a complete characterization of the complexity bounds—both upper and lower—for equilibrium realizability and verification problems. Our results demonstrate that the proposed circuit-based model is provably superior in theoretical expressiveness and computational properties compared to conventional explicit representations.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Recent work in the field of multi-agent systems has sought to use techniques and concepts from the field of formal methods to provide rigorous theoretical analysis and guarantees on complex systems where multiple agents strategically interact, leading to the creation of the field of equilibrium analysis, which studies equilibria concepts from the field of game theory through a complexity-theoretic lens. Multi-agent systems, however, are complex mathematical objects, and, therefore, defining them in a precise mathematical manner is non-trivial. As a result, researchers often considered more restrictive models that are easier to model but lack expressive power or simply omit critical complexity-theoretic results in their analysis. This paper addresses this problem by carefully analyzing and contrasting complexity-theoretic results in the explicit model, a mathematically precise formulation of the models commonly used in the literature, and the circuit-based model, a novel model that addresses the problems found in the literature. The utility of the circuit-based model is demonstrated through a comprehensive analysis that considers upper and lower bounds for the realizability and verification problems, the two most important decision problems in equilibrium analysis, for both models. By conducting this analysis, we see that problematic issues that are endemic to the explicit model and the equilibrium analysis literature as a whole are adequately handled by the circuit-based model.

Problem

• multi-agent systems
• formal modeling
• complexity-theoretic analysis
• equilibrium analysis
• expressiveness

Innovation

• circuit-based model
• equilibrium analysis
• multi-agent systems
• complexity-theoretic analysis
• formal methods