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Article information
2020 , Volume 25, ¹ 4, p.31-44
Kornienko V.S., Shaidurov V.V., Karepova E.D.
A finite difference analogue of the "mean field" equilibrium problem
In most forecasting problems, overstating or understating forecast leads to various losses. Traditionally, in the theory of “mean field games”, the functional responsible for the costs of implementing the interaction of the continuum of agents between each other is supposed to be dependent on the squared function of control of the system. Since additional external factors can influence the player’s strategy, the control function of a dynamic system is more complex. Therefore, the purpose of this article is to develop a computational algorithm applicable for more general set of control functions. As a research method, a computational experiment and proof of the stability of the constructed computational scheme are used in this study. As a result, the numerical algorithm was applied on the problem of economic interaction in the presence of alternative resources. We consider the model, in which a continuum of consumer agents consists of households deciding on heating, having a choice between the cost of installing and maintaining the thermal insulation or the additional cost of electricity. In the framework of the problem, the convergence of the method is numerically demonstrated. Conclusions. The article considers a model of the strategic interaction of continuum of agents, the interaction of which is determined by a coupled differential equations, namely, the Fokker — Planck and the Hamilton — Jacobi — Bellman one. To approximate the differential problem, difference schemes with a semi-Lagrangian approximation are used, which give a direct rule for minimizing the cost functional
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Keywords: optimal control, mean field game, numerical methods, finite differences, economic problems
doi: 10.25743/ICT.2020.25.4.004
Author(s):
Kornienko Viktoriya Sergeevna
Position: Junior Research Scientist
Office: Institute of Computational Modeling Siberian Branch of the Russian Academy of Sciences
Address: 660036, Russia, Krasnoyarsk, str. Akademgorodok, 50/44
E-mail: vika-svetlakova@yandex.ru
Shaidurov Vladimir Victorovich
Dr. , Correspondent member of RAS, Professor
Position: Head of Research
Office: Federal Research Center Krasnoyarsk Science Center of the Siberian Branch of the Russian Academy of Science
Address: 660036, Russia, Krasnoyarsk 36, Akademgorodok 50, building 44
Phone Office: (391) 243 27 56
E-mail: shaidurov04@gmail.com
SPIN-code: 7075-6423Karepova Evgeniya Dmitrievna
PhD. , Associate Professor
Position: Head of Departament
Office: Institute of Computational Modeling of SB RAS
Address: 660036, Russia, Krasnoyarsk, str. Akademgorodok, 50/44
Phone Office: (391) 243 27 56
E-mail: e.d.karepova@icm.krasn.ru
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Bibliography link:
Kornienko V.S., Shaidurov V.V., Karepova E.D. A finite difference analogue of the "mean field" equilibrium problem // Computational technologies. 2020. V. 25. ¹ 4. P. 31-44
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