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Mat. Sb., 2015, Volume 206, Number 7, Pages 3–32 (Mi msb8380)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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).


DOI: https://doi.org/10.4213/sm8380

Full text: PDF file (630 kB)
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English version:
Sbornik: Mathematics, 2015, 206:7, 893–920

Bibliographic databases:

Document Type: Article
UDC: 517.978.4
MSC: Primary 91A06, 91A13, 91A23; Secondary 49N70
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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. Averboukh, “A property of the value multifunction of the deterministic mean-field game”, Proceedings of the 8th International Conference on Mathematical Modeling (ICMM-2017), AIP Conf. Proc., 1907, Amer. Inst. Phys., 2017, UNSP 030048-1  crossref  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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