Computation of Mean-Field Equilibria with Correlated Stochastic Processes

  • V. ShaydurovEmail author
  • S. Zhang
  • V. Kornienko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


The numerical algorithm is presented for solving differential problem formulated as the Mean-Field Game (MFG) with the coupled system of two parabolic partial differential equations: the Fokker-Plank-Kolmogorov equation and the Hamilton-Jacobi-Bellman one. The case is considered with correlation of the considered stochastic processes. The description focuses on the discrete semi-Lagrangian approximation of these equations and on the application of the MFG theory directly at discrete level. The constructed algorithm is implemented to the problem of carbon dioxide pollution as an illustration.


Optimal control Mean-Field Game Numerical approximation Finite differences Carbon dioxide pollution 


  1. 1.
    Lasry, J.M., Lions, P.L.: Jeux champ moyen. I. Le cas stationnaire. C. R. Math. Acad. Sci. Paris 343(9), 619–625 (2006)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Lasry, J.M., Lions, P.L.: Jeux champ moyen. II. Horizon fini et contrle optimal. C. R. Math. Acad. Sci. Paris 343(10), 679–684 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bensoussan, A., Frehse, J., Yam, P.: Mean Field Games and Mean Field Type Control Theory. Springer, Berlin (2013). Scholar
  4. 4.
    Shaydurov, V., Zhang, S., Karepova, E.: Conservative difference schemes for the computation of mean-field equilibria. In: AIP Conference Proceedings, vol. 1892, pp. 20–35 (2017)Google Scholar
  5. 5.
    Röhl, T., Röhl, C., Schuster, H.C., Traulsen, A.: Impact of fraud on the mean-field dynamics of cooperative social systems. Phys. Rev. E 76, 026114 (2007)CrossRefGoogle Scholar
  6. 6.
    Chang, S., Wang, X.: Modeling and computation of mean field equilibria in producers game with emission permits trading. Commun. Nonlinear Sci. Numer. Simulat. 37, 238–248 (2016)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Shaydurov, V., Vyatkin, A., Kuchunova, E.: Semi-Lagrangian difference approximations with different stability requirements. Russ. J. Numer. Anal. Math. Model. 33(2), 123–135 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Tianjin University of Finance and EconomicsTianjinChina
  2. 2.Institute of Computational Modeling of SB RASKrasnoyarskRussia
  3. 3.Siberian Federal UniversityKrasnoyarskRussia

Personalised recommendations