Düring, Bertram, Torregrossa, Marco and Wolfram, Marie-Therese (2019) Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects. Journal of Nonlinear Science, 29 (3). pp. 1095-1128. ISSN 0938-8974
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Abstract
In this paper we propose and study a new kinetic rating model for a large number of players, which is motivated by the well-known Elo rating system. Each player is characterised by an intrinsic strength and a rating, which are both updated after each game. We state and analyse the respective Boltzmann type equation and derive the corresponding nonlinear, nonlocal Fokker-Planck equation. We investigate the existence of solutions to the Fokker-Planck equation and discuss their behaviour in the long time limit. Furthermore, we illustrate the dynamics of the Boltzmann and Fokker-Planck equation with various numerical experiments.
Item Type: | Article |
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Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Research Centres and Groups: | Numerical Analysis and Scientific Computing Research Group |
Depositing User: | Alice Jackson |
Date Deposited: | 27 Nov 2018 12:43 |
Last Modified: | 16 Mar 2021 10:37 |
URI: | http://sro.sussex.ac.uk/id/eprint/80449 |
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📧 Request an updateProject Name | Sussex Project Number | Funder | Funder Ref |
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Novel discretisations of higher-order nonlinear PDE | G1603 | LEVERHULME TRUST | RPG-2015-069 |
New Frontier’s Grant | Unset | Austrian Academy of Sciences | NST 0001 |
EPSRC | Unset | Unset | EP/P01240X/1. |