## 2012 Young Researchers Workshop:Kinetic Description of Multiscale Phenomena

### Continuous models for rating systems and their long time behavior

Pierre-Emmanuel Jabin

University of Maryland

Abstract:

We present some rating systems, like ELO for chess or tennis. We derive their limit when the number of players is large and study the long time behavior of the corresponding equations. We can show that the rating systems effectively "work" in the sense that the score attributed to each player converge to their intrinsic strength.