Multi-Agent Systems

Kinetic Description of Multi-Agent Systems, SS 2019

Dr. Torsten Trimborn

A class for students of CES and Mathematics, as well as everybody interested.


We study the mathematical description of multi-agent systems on different modeling levels. Especially we discuss the passage from microscopic agent dynamics to kinetic equations (e.g. Boltzmann) and the passage from mesoscopic equations to macroscopic equations (e.g. Euler). Such kinetic formulations play an important role in a variety of physical, biological and social applications. Furthermore, we discuss Monte-Carlo methods for kinetic equations and study the possibility to add an optimization problem to the microscopic dynamics.

  • Kinetic equations (Boltzmann, Vlasov-Poisson)
  • Kinetic limits (mean field limit, Boltzmann-Grad limit, grazing limit)
  • Analytical properties (existence, uniqueness, h-theorem)
  • Boltzmann to Euler and Navier-Stokes
  • Monte-Carlo methods for kinetic equations
  • Mean field games


The formal structure of the class will be one lecture each week and a tutorial every second week.

The times for lectures and tutorials are given below.

  • Tuesdays (usually lecture), 10:30 - 12:00, in 1090(Rogowski)|328
  • Thursday (usually tutorial), 14:30 - 16:00, in 1090(Rogowski)|328

There are 5 ECTS points to earn with an oral exam of 30min.

See also Also, please register with the L2P-Room, available at RWTH E-Learning.

Some Background Literature

For further readings we recommend the following literature. For sure many books actually go far beyond the course material. But they certainly resonate with what is done in the course.

  • H. Babovsky, Die Boltzmann-Gleichung, Teubner, 1998
  • H. Spohn, Large scale dynamics of interacting particles, Springer-Verlag,1991
  • P. Cardaliague, Notes on Mean Field Games, 2013
  • L. Pareschi and G. Toscani, Interacting Multiagent Systems, 2013

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Last modified:: 2019/09/26 13:45