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Mean Field Games for Diel Vertical Migration with Diffusion
We present a theoretical framework, based on differential mean field games, for expressing diel vertical migration in the ocean as a game with a continuum of players. In such a game, each agent partially controls its own state by adjusting its vertical velocity but the vertical position in a water c...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10140133/ https://www.ncbi.nlm.nih.gov/pubmed/37106263 http://dx.doi.org/10.1007/s11538-023-01154-3 |
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author | Mazuryn, Maksim Thygesen, Uffe Høgsbro |
author_facet | Mazuryn, Maksim Thygesen, Uffe Høgsbro |
author_sort | Mazuryn, Maksim |
collection | PubMed |
description | We present a theoretical framework, based on differential mean field games, for expressing diel vertical migration in the ocean as a game with a continuum of players. In such a game, each agent partially controls its own state by adjusting its vertical velocity but the vertical position in a water column is also subject to random fluctuations. A representative player has to make decisions based on aggregated information about the states of the other players. For this vertical differential game, we derive a mean field system of partial differential equations for finding a Nash equilibrium for the whole population. It turns out that finding Nash equilibria in the game is equivalent to solving a PDE-constrained optimization problem. We detail this equivalence when the expected fitness of the representative player can be approximated with a constant and solve both formulations numerically. We illustrate the results on simple numerical examples and construct several test cases to compare the two analytical approaches. |
format | Online Article Text |
id | pubmed-10140133 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-101401332023-04-29 Mean Field Games for Diel Vertical Migration with Diffusion Mazuryn, Maksim Thygesen, Uffe Høgsbro Bull Math Biol Original Article We present a theoretical framework, based on differential mean field games, for expressing diel vertical migration in the ocean as a game with a continuum of players. In such a game, each agent partially controls its own state by adjusting its vertical velocity but the vertical position in a water column is also subject to random fluctuations. A representative player has to make decisions based on aggregated information about the states of the other players. For this vertical differential game, we derive a mean field system of partial differential equations for finding a Nash equilibrium for the whole population. It turns out that finding Nash equilibria in the game is equivalent to solving a PDE-constrained optimization problem. We detail this equivalence when the expected fitness of the representative player can be approximated with a constant and solve both formulations numerically. We illustrate the results on simple numerical examples and construct several test cases to compare the two analytical approaches. Springer US 2023-04-27 2023 /pmc/articles/PMC10140133/ /pubmed/37106263 http://dx.doi.org/10.1007/s11538-023-01154-3 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Original Article Mazuryn, Maksim Thygesen, Uffe Høgsbro Mean Field Games for Diel Vertical Migration with Diffusion |
title | Mean Field Games for Diel Vertical Migration with Diffusion |
title_full | Mean Field Games for Diel Vertical Migration with Diffusion |
title_fullStr | Mean Field Games for Diel Vertical Migration with Diffusion |
title_full_unstemmed | Mean Field Games for Diel Vertical Migration with Diffusion |
title_short | Mean Field Games for Diel Vertical Migration with Diffusion |
title_sort | mean field games for diel vertical migration with diffusion |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10140133/ https://www.ncbi.nlm.nih.gov/pubmed/37106263 http://dx.doi.org/10.1007/s11538-023-01154-3 |
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