Kinetic Theory, Mean Field Game and Applications
Student No.:50
Time:Mon/Wed 10 :10-12 :00am, 07-15~08-12
Instructor:Jian-Guo Liu  [Duke University]
Place:Conference Room 4,Floor 2, Jin Chun Yuan West Building
Starting Date:2013-7-15
Ending Date:2013-8-12



The place of lecture from July 29 to August 2th will be changed to room A304 of Math department.




In this short course, I will introduce some recent results on mathematical analysis of collective dynamics, decision making and self-organization in complex systems coming from biology and social sciences. We will use agent based kinetic equations to model some social behaviors such as opinion formulation, evolution of the distribution of wealth, pedestrian traffic flow, collective dynamics, flow on sweeping networks, etc.


The fast and frequent local self-interactions between agents such as opinion exchanging, cellular automata network switching, economic activities, lead to a local Nash equilibrium for the distribution of the agents.

This Nash equilibrium gives a macroscopic closure and leads to some simple partial differential equations modeling these social behaviors.


Emergence phenomena of the collective dynamics is studied through the investigation of phase transition and stability of these Nash equilibria.






 D. Monderer, L. S. Shapley, Potential Games, Games and Economic Behavior, 14 (1996), 124--143.


Castellano, C., Fortunato, S., and Loreto, V. Statistical physics of social dynamics. Reviews of Modern Physics, 81(2009) 591--646.


P Degond, J-G Liu, C Ringhofer, A Nash equilibrium macroscopic closure for kinetic models based on mean-field-games, preprint.


P Degond, J-G Liu, C Ringhofer, Evolution of the distribution of wealth in economic neighborhood by local Nash equilibrium closure, preprint.


P Degond, A Frouvelle, J-G Liu, S Motsch, L Navoret, Macroscopic models of collective motion and self-organization, preprint.


P Degond, A Frouvelle, J-G Liu, Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics, preprint








P. Cardaliaguet, Notes on Mean Field Games (from P.-L. Lions' lectures at College de France), 2012.


J.-M. Lasry, P.-L. Lions, Mean field games, Japan J. Math. 2 (2007) 229--260.


J.-P. Bouchaud, M. Mezard, Wealth condensation in a simple model of economy, Physica A 282 (2000) 536--545.