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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
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.
Received: 21.04.2014 and 22.01.2015
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
Linking options:
https://www.mathnet.ru/eng/sm8380https://doi.org/10.1070/SM2015v206n07ABEH004482 https://www.mathnet.ru/eng/sm/v206/i7/p3
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Abstract page: | 691 | Russian version PDF: | 190 | English version PDF: | 35 | References: | 92 | First page: | 58 |
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