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

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posted on 2023-06-09, 16:01 authored by Bertram Duering, Marco Torregrossa, Marie-Therese Wolfram
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.

Funding

EPSRC; EP/P01240X/1.

New Frontier’s Grant; Austrian Academy of Sciences; NST 0001

Novel discretisations of higher-order nonlinear PDE; G1603; LEVERHULME TRUST; RPG-2015-069

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Nonlinear Science

ISSN

0938-8974

Publisher

Springer Verlag

Issue

3

Volume

29

Page range

1095-1128

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Numerical Analysis and Scientific Computing Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-11-27

First Open Access (FOA) Date

2018-11-27

First Compliant Deposit (FCD) Date

2018-11-26

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