Кондакова Е.А.   Криворотько О.И.   Кабанихин С.И.  

Numerical methods for solution of the inverse problem of mean field games

Докладчик: Кондакова Е.А.

Numerical methods for solution of the inverse problem of mean field games
Kondakova E.A.1,2, Krivorotko O.I.1,2, Kabanikhin S.I. 1,2
1 Novosibirsk State University,
2 Institute of Computational Mathematics and Mathematical Geophysics SB RAS
E-mail: ekondak95@mail.ru, olga.krivorotko@sscc.ru, kabanikhin@sscc.ru

Major global events shaped by large populations in social media, such as the Arab Spring, the Black Lives Matter movement, and the fake news controversy during the 2016 U.S. presidential election, provide significant impetus for devising new models that account for macroscopic population behavior resulting from the aggregate decisions and actions taken by all individuals. Mean fields games describe the analysis of differential games in which the number of players tends to plus infinite [1-2]. The paper considers numerical methods for the problem of optimal planning, i.e. the problem in which the positions of a very large number of identical rational agents, with common value function, evolve from a given initial spatial density to a desired target density at the final horizon time. The results of the numerical calculations for the mathematical model of social media are presented and discussed.
The work has been supported by the grant of the President of RF (no. MK-1214.2017.1), Ministry of Education and Science of Russian Federation and by the grant of the RSF (no. 18-71-10044).
1. Achdou Y., Camilli F., Capuzzo-Dolcetta I. Mean field games: numerical methods for the planning problem. Pre-publication. 2010.
2. Lions P.-L. Notes on Mean Field Games // Lecture at Tor Vergata University. 2013.

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