On the Nucleolus of a Class of Linear Production Games
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866912564110163968 |
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| author | Baïou, Mourad Oriolo, Gianpaolo Stauffer, Gautier |
| author_facet | Baïou, Mourad Oriolo, Gianpaolo Stauffer, Gautier |
| contents | We study the nucleolus in a class of cooperative games where agents collaborate by sharing demands and production-distribution capacities across multiple markets. These production-distribution games form a structured subclass of linear production games and capture applications such as horizontal collaboration in logistics. While computing the nucleolus is generally NP-hard for linear production games, we show that structural properties of production-distribution games enable efficient computation in several cases. Our main results focus on the uncapacitated variant. First, we provide a polynomial-time characterization of instances where the core reduces to a singleton, allowing direct computation of the nucleolus. Second, when the number of markets is fixed, we design a separation-based polynomial-time algorithm. Third, in the single-market case, we develop a faster combinatorial primal-dual algorithm that runs in $O(n^4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04105 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Nucleolus of a Class of Linear Production Games Baïou, Mourad Oriolo, Gianpaolo Stauffer, Gautier Computer Science and Game Theory Discrete Mathematics Optimization and Control We study the nucleolus in a class of cooperative games where agents collaborate by sharing demands and production-distribution capacities across multiple markets. These production-distribution games form a structured subclass of linear production games and capture applications such as horizontal collaboration in logistics. While computing the nucleolus is generally NP-hard for linear production games, we show that structural properties of production-distribution games enable efficient computation in several cases. Our main results focus on the uncapacitated variant. First, we provide a polynomial-time characterization of instances where the core reduces to a singleton, allowing direct computation of the nucleolus. Second, when the number of markets is fixed, we design a separation-based polynomial-time algorithm. Third, in the single-market case, we develop a faster combinatorial primal-dual algorithm that runs in $O(n^4)$. |
| title | On the Nucleolus of a Class of Linear Production Games |
| topic | Computer Science and Game Theory Discrete Mathematics Optimization and Control |
| url | https://arxiv.org/abs/2211.04105 |