"Mean field games" as mathematical models for control and optimization of business activity

Тип публикации: статья из журнала

Год издания: 2019

Идентификатор DOI: 10.17516/1997–1370–0418

Ключевые слова: Hamilton-Jacobi-Bellman equation, Kolmogorov equation, Mathematical economical models, Mean Field Games, Numerical solution

Аннотация: The article is a review of modern mathematical economic models with the "Mean Field Games" structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefit. © Siberian Federal University. All rights reserved.

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Издание

Журнал: Journal of Siberian Federal University - Humanities and Social Sciences

Выпуск журнала: Vol. 12, Is. 4

Номера страниц: 701-715

ISSN журнала: 19971370

Издатель: Siberian Federal University

Авторы

  • Shaidurov V.V. (Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation, Tianjin University of Finance and Economics, 25 Zhujiang Road, Hexi District, Tianjin, 300222, China)
  • Kornienko V.S. (Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, Krasnoyarsk, 660036, Russian Federation, Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041, Russian Federation)

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