  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.
