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In this paper we study the long-time behaviour of a kinetic formulation of anElo-type rating model for a large number of interacting players with variablestrength. The model results in a non-linear mean-field Fokker-Planck equationand 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 hypocoercivitytechniques.

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