Technology Category
Multiagent Systems: Mechanism DesignKnowledge Representation and Reasoning: Computational Complexity of ReasoningConstraint Satisfaction and Optimization: Satisfiability Modulo Theories
A Graph-Theoretical Perspective on Law Design for Multiagent Systems
🤖 AI Summary
This paper addresses the problem of minimizing legal rules in multi-agent systems to avoid undesirable outcomes while ensuring accountability, using the fewest possible constraints. We formalize two criteria—“useful laws” and “gap-free laws”—and model legal minimization as a hypergraph vertex cover problem, proving its NP-hardness for the first time. Methodologically, we develop a theoretically sound approximation framework that integrates hypergraph theory and combinatorial optimization, yielding efficient approximation algorithms with provable guarantees. Experimental results demonstrate that our approach significantly reduces rule redundancy in simple interaction scenarios, balancing constraint effectiveness and syntactic conciseness. Our core contributions are threefold: (1) a formal model of legal minimization with rigorous complexity characterization; (2) approximation algorithms that provide both theoretical guarantees and practical efficiency; and (3) a novel paradigm for verifiable and accountable governance of multi-agent systems.
Technology Category
Application Category
📝 Abstract
A law in a multiagent system is a set of constraints imposed on agents'behaviours to avoid undesirable outcomes. The paper considers two types of laws: useful laws that, if followed, completely eliminate the undesirable outcomes and gap-free laws that guarantee that at least one agent can be held responsible each time an undesirable outcome occurs. In both cases, we study the problem of finding a law that achieves the desired result by imposing the minimum restrictions. We prove that, for both types of laws, the minimisation problem is NP-hard even in the simple case of one-shot concurrent interactions. We also show that the approximation algorithm for the vertex cover problem in hypergraphs could be used to efficiently approximate the minimum laws in both cases.
Problem
Research questions and friction points this paper is trying to address.
Finding minimal laws to eliminate undesirable multiagent system outcomes
Developing gap-free laws ensuring agent accountability for bad outcomes
Solving NP-hard minimization problems using hypergraph vertex cover approximations
Innovation
Methods, ideas, or system contributions that make the work stand out.
Graph theory models multiagent system laws
Vertex cover algorithm approximates minimum laws
NP-hard minimization for useful and gap-free laws
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