Learning equilibria in Cournot mean field games of controls
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916458635722752 |
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| author | Camilli, Fabio Laurière, Mathieu Tang, Qing |
| author_facet | Camilli, Fabio Laurière, Mathieu Tang, Qing |
| contents | We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function. Then, we prove convergence of a learning algorithm which gives existence of a solution to the mean field games system. The learning algorithm is implemented with a suitable finite difference discretization to get a numerical method to the solution. We supplement our theoretical analysis with several numerical examples and illustrate the impacts of model parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Learning equilibria in Cournot mean field games of controls Camilli, Fabio Laurière, Mathieu Tang, Qing Optimization and Control Analysis of PDEs We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function. Then, we prove convergence of a learning algorithm which gives existence of a solution to the mean field games system. The learning algorithm is implemented with a suitable finite difference discretization to get a numerical method to the solution. We supplement our theoretical analysis with several numerical examples and illustrate the impacts of model parameters. |
| title | Learning equilibria in Cournot mean field games of controls |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2405.01812 |