A Gauss-Seidel method for solving multi-leader-multi-follower games
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910691093381120 |
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| author | Franci, Barbara Fabiani, Filippo Schmidt, Martin Staudigl, Mathias |
| author_facet | Franci, Barbara Fabiani, Filippo Schmidt, Martin Staudigl, Mathias |
| contents | We design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer optimization and the characterization of variational equilibria in terms of the Karush-Kuhn-Tucker conditions, we propose a mixed-integer game formulation for solving this challenging class of problems. Besides providing an equivalent reformulation, we design a proximal Gauss--Seidel method with global convergence guarantees in case the game enjoys a potential structure. We finally corroborate the numerical performance of the algorithm on a novel instance of the ride-hail market problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02605 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Gauss-Seidel method for solving multi-leader-multi-follower games Franci, Barbara Fabiani, Filippo Schmidt, Martin Staudigl, Mathias Optimization and Control We design a computational approach to find equilibria in a class of Nash games possessing a hierarchical structure. By using tools from mixed-integer optimization and the characterization of variational equilibria in terms of the Karush-Kuhn-Tucker conditions, we propose a mixed-integer game formulation for solving this challenging class of problems. Besides providing an equivalent reformulation, we design a proximal Gauss--Seidel method with global convergence guarantees in case the game enjoys a potential structure. We finally corroborate the numerical performance of the algorithm on a novel instance of the ride-hail market problem. |
| title | A Gauss-Seidel method for solving multi-leader-multi-follower games |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.02605 |