Steady states of an Elo-type rating model for players of varying strength
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866916172484575232 |
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| author | Düring, Bertram Evans, Josephine Wolfram, Marie-Therese |
| author_facet | Düring, Bertram Evans, Josephine Wolfram, Marie-Therese |
| contents | In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model results in a non-linear mean-field Fokker-Planck equation and we show the existence of steady states via a Schauder fixed point argument. Our proof relies on the study of a related linear equation using hypocoercivity techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_10260 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Steady states of an Elo-type rating model for players of varying strength Düring, Bertram Evans, Josephine Wolfram, Marie-Therese Analysis of PDEs In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model results in a non-linear mean-field Fokker-Planck equation and we show the existence of steady states via a Schauder fixed point argument. Our proof relies on the study of a related linear equation using hypocoercivity techniques. |
| title | Steady states of an Elo-type rating model for players of varying strength |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2204.10260 |