Collective Behavior: Macroscopic versus Kinetic Descriptions

Asymptotic behavior in opinion formation and rating systems

Pierre-Emmanuel Jabin

University of Maryland

We present here results about the convergence in time of two classes of models: Opinion formation like the so-called Krause model and rating systems which try to evaluate a player strength (as in the ELO system). In both cases, it is hoped that convergence to a unique equilibrium would hold; representing either a commonly shared opinion or a rating evaluation which precisely coincide with the player strength. However in most realistic cases, the interaction between agents or players is compactly supported creating puzzling meta-stable phenomena. It is nevertheless possible to prove the convergence to a final equilibrium with however a more complicated structure than in the cases with non vanishing interactions. This corresponds to two joint works with S. Junca and S. Motsch.