Journal of Nonlinear Science

, Volume 24, Issue 1, pp 93–115 | Cite as

Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria

  • Pierre DegondEmail author
  • Jian-Guo Liu
  • Christian Ringhofer


We introduce a new mean field kinetic model for systems of rational agents interacting in a game-theoretical framework. This model is inspired from non-cooperative anonymous games with a continuum of players and Mean-Field Games. The large time behavior of the system is given by a macroscopic closure with a Nash equilibrium serving as the local thermodynamic equilibrium. An application of the presented theory to a social model (herding behavior) is discussed.


Non-cooperative non-atomic anonymous games Continuum of players Rational agent Best-reply scheme Local Nash equilibrium Potential games Social herding behavior Coarse graining procedure Macroscopic closure Kinetic theory 

Mathematics Subject Classification

91A10 91A13 91A40 82C40 82C21 



This work has been supported by KI-Net NSF RNMS grant No. 1107291. JGL and CR are grateful for the opportunity to stay and work at the Institut de Mathématiques de Toulouse in fall 2012, under sponsorship from Centre National de la Recherche Scientifique and University Paul-Sabatier. The authors wish to thank A. Blanchet from University Toulouse 1 Capitole for enlightening discussions.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Pierre Degond
    • 1
    • 2
    Email author
  • Jian-Guo Liu
    • 3
  • Christian Ringhofer
    • 4
  1. 1.UPS, INSA, UT1, UTM, Institut de Mathématiques de ToulouseUniversité de ToulouseToulouseFrance
  2. 2.Institut de Mathématiques de Toulouse UMR 5219CNRSToulouseFrance
  3. 3.Department of Physics and Department of MathematicsDuke UniversityDurhamUSA
  4. 4.School of Mathematics and Statistical SciencesArizona State UniversityTempeUSA

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