  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.
