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Sbornik: Mathematics, 2015, Volume 206, Issue 7, Pages 893–920
DOI: https://doi.org/10.1070/SM2015v206n07ABEH004482 (Mi sm8380) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A minimax approach to mean field games

Yu. V. Averboukhab

a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University, Ekaterinburg
English version PDF (592 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM2015v206n07ABEH004482
Abstract: An initial boundary value problem for the system of equations of a determined mean field game is considered. The proposed definition of a generalized solution is based on the minimax approach to the Hamilton-Jacobi equation. We prove the existence of the generalized (minimax) solution using the Nash equilibrium in the auxiliary differential game with infinitely many identical players. We show that the minimax solution of the original system provides the $\varepsilon$-Nash equilibrium in the differential game with a finite number of players.
Bibliography: 34 titles.
Keywords: mean-field-games, Hamilton-Jacobi equations, minimax solution, Nash equilibrium, differential game with infinitely many players.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-07909
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 15-01-07909).
Received: 21.04.2014 and 22.01.2015
Russian version:
Matematicheskii Sbornik, 2015, Volume 206, Number 7, Pages 3–32
DOI: https://doi.org/10.4213/sm8380
Bibliographic databases:
Document Type: Article
UDC: 517.978.4
MSC: Primary 91A06, 91A13, 91A23; Secondary 49N70
Language: English
Original paper language: Russian
Citation: Yu. V. Averboukh, “A minimax approach to mean field games”, Mat. Sb., 206:7 (2015), 3–32; Sb. Math., 206:7 (2015), 893–920
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:92
    First page:58
     
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