Approximations of two-dimensional Mean Field Games with nonsymmetric controls
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URI (для ссылок/цитирований):
https://www.sciencedirect.com/science/article/abs/pii/S0377042719304649https://elib.sfu-kras.ru/handle/2311/142929
Автор:
Shaydurov, V.
Zhang, S.
Kornienko, V.
Коллективный автор:
Институт математики и фундаментальной информатики
Базовая кафедра вычислительных и информационных технологий
Дата:
2020-03Журнал:
Journal of Computational and Applied MathematicsКвартиль журнала в Scopus:
Q2Квартиль журнала в Web of Science:
Q1Библиографическое описание:
Shaydurov, V. Approximations of two-dimensional Mean Field Games with nonsymmetric controls [Текст] / V. Shaydurov, S. Zhang, V. Kornienko // Journal of Computational and Applied Mathematics. — 2020. — Т. 367 (№ 15). — С. 112461Текст статьи не публикуется в открытом доступе в соответствии с политикой журнала.
Аннотация:
The numerical methods are presented for solving economic problems formulated in
the Mean-Field Game (MFG) form. The mean-field equilibrium is a solution of the
coupled system of two parabolic partial differential equations: the Fokker–Planck–
Kolmogorov equation and the Hamilton–Jacobi–Bellman one. The description focuses
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 functions. Contrary to other difference schemes, here
the semi-Lagrangian approximation is applied, which improves properties of a discrete
problem of this type. This implies the fast convergence of an iterative algorithm for the
minimization of the cost functional. The constructed algorithms are implemented to the
problem of carbon dioxide pollution.