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

Autor:	Düring, Bertram, Torregrossa, Marco, Wolfram, Marie-Therese
Rok vydání:	2018
Předmět:	Physics - Physics and Society Mathematics - Analysis of PDEs Nonlinear Sciences - Adaptation and Self-Organizing Systems 35Q84 35Q20 35Q91 70F45 82B21 82B26 82C22
Zdroj:	J. Nonlinear Sci. 29(3), 1095-1128, 2019
Druh dokumentu:	Working Paper
DOI:	10.1007/s00332-018-9512-8
Popis:	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. Comment: 24 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1806.06648 Zobrazit plný text záznamu View this record from Arxiv