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 ε-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.
\Bibitem{Ave15}
\by Yu.~V.~Averboukh
\paper A minimax approach to mean field games
\jour Sb. Math.
\yr 2015
\vol 206
\issue 7
\pages 893--920
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https://www.mathnet.ru/eng/sm8380
https://doi.org/10.1070/SM2015v206n07ABEH004482
https://www.mathnet.ru/eng/sm/v206/i7/p3
This publication is cited in the following 4 articles:
Gomoyunov M.I., “Minimax Solutions of Hamilton-Jacobi Equations With Fractional Coinvariant Derivatives”, ESAIM-Control OPtim. Calc. Var., 28 (2022), 23
Yu. Averboukh, “Viability analysis of the first-order mean field games”, ESAIM-Control OPtim. Calc. Var., 26 (2020), UNSP 33
Yu. Averboukh, “Deterministic limit of mean field games associated with nonlinear Markov processes”, Appl. Math. Optim., 81:3 (2020), 711–738
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
Citation in format AMSBIB
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