Steady states of an Elo-type rating model for players of varying strength

Abstract

In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model results in a non-linear mean-field Fokker-Planck equation and we show the existence of steady states via a Schauder fixed point argument. Our proof relies on the study of a related linear equation using hypocoercivity techniques.

2 figures, 20 pages

References in corpus (2)

• On a kinetic opinion formation model for pre-election polling
• An Elo-type rating model for players and teams of variable strength