A Graph-Theoretical Perspective on Law Design for Multiagent Systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912816672276480 |
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| author | Shi, Qi Naumov, Pavel |
| author_facet | Shi, Qi Naumov, Pavel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Graph-Theoretical Perspective on Law Design for Multiagent Systems Shi, Qi Naumov, Pavel Multiagent Systems Artificial Intelligence Computer Science and Game Theory 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. |
| title | A Graph-Theoretical Perspective on Law Design for Multiagent Systems |
| topic | Multiagent Systems Artificial Intelligence Computer Science and Game Theory |
| url | https://arxiv.org/abs/2511.06361 |