Conservative difference schemes for the computation of mean-field equilibria

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: ??9th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'17; Albena, Bulgaria; Albena, Bulgaria

Год издания: 2017

Идентификатор DOI: 10.1063/1.5007358

Аннотация: The numerical methods are presented for solving economic problems formulated in the Mean Field Game (MFG) form. The mean-field equilibrium (i.e., the Nash equilibrium for an infinite number of players) leads to the coupled system of two parabolic partial differential equations: the Hamilton-Jacobi-Bellman-Isaacs equation and the Fokker-Planck-Kolmogorov one. The description is focused on the discrete approximation of these equations and on the application of the MFG theory directly at discrete level. This approach results in an efficient algorithm for finding the corresponding grid control function. Contrary to difference schemes with directed differences used by other authors, here the semi-Lagrangian approximation is applied which improves some properties of a discrete problem of this type. This implies the fast convergence of an iterative algorithm for the monotone minimization of the cost functional.

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Издание

Журнал: AIP CONFERENCE PROCEEDINGS

Выпуск журнала: 1895

Номера страниц: 020004-020004

Издатель: American Institute of Physics Inc.

Авторы

  • Shaydurov V. (Krasnoyarsk Science Centre of the Siberian Branch of Russian Academy of Science)
  • Zhang S. (Tianjin University of Finance and Economics)
  • Karepova E. (Krasnoyarsk Science Centre of the Siberian Branch of Russian Academy of Science)

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