Boltzmann and Fokker-Planck equations modelling the Elo rating system with learning effects

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
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: 01 Jul 2019 15:18
URI: http://sro.sussex.ac.uk/id/eprint/80449

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Project NameSussex Project NumberFunderFunder Ref
Novel discretisations of higher-order nonlinear PDEG1603LEVERHULME TRUSTRPG-2015-069
New Frontier’s GrantUnsetAustrian Academy of SciencesNST 0001
EPSRCUnsetUnsetEP/P01240X/1.