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

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arxiv 1806.06648 v2 pith:WNDJNTJ3 submitted 2018-06-18 physics.soc-ph math.APnlin.AO

Bertram Düring , Marco Torregrossa , Marie-Therese Wolfram This is my paper · ORCID
classification physics.soc-phmath.APnlin.AO
keywords equationfokker-planckratingboltzmannsystemanalysebehaviourcharacterised
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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.

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  1. Elo Ratings in the Presence of Intransitivity

    math.PR 2024-12 conditional novelty 7.0 of 10

    Elo ratings in intransitive games are unique for a given schedule but shift with the schedule, so they cannot represent a single transitive skill scale.

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