Two-scale homogenization of a stationary mean-field game

Rita Ferreira; Diogo A. Gomes; Xianjin Yang

doi:10.1051/cocv/2020002

Two-scale homogenization of a stationary mean-field game

Rita Ferreira, Diogo A. Gomes, Xianjin Yang

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.

Original language	English (US)
Pages (from-to)	17
Journal	ESAIM: Control, Optimisation and Calculus of Variations
Volume	26
DOIs	https://doi.org/10.1051/cocv/2020002
State	Published - Feb 14 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-CRG2017-3452
Acknowledgements: The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.

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10.1051/cocv/2020002

https://repository.kaust.edu.sa/bitstream/10754/660832/4/FerreiraGomesYang_MFGHomog.pdf

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title = "Two-scale homogenization of a stationary mean-field game",

abstract = "In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.",

author = "Rita Ferreira and Gomes, {Diogo A.} and Xianjin Yang",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): OSR-CRG2017-3452 Acknowledgements: The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.",

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T1 - Two-scale homogenization of a stationary mean-field game

AU - Ferreira, Rita

AU - Gomes, Diogo A.

AU - Yang, Xianjin

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): OSR-CRG2017-3452 Acknowledgements: The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.

PY - 2020/2/14

Y1 - 2020/2/14

N2 - In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.

AB - In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.

UR - http://hdl.handle.net/10754/660832

UR - https://www.esaim-cocv.org/10.1051/cocv/2020002

U2 - 10.1051/cocv/2020002

DO - 10.1051/cocv/2020002

M3 - Article

SN - 1292-8119

VL - 26

SP - 17

JO - ESAIM: Control, Optimisation and Calculus of Variations

JF - ESAIM: Control, Optimisation and Calculus of Variations

ER -

Two-scale homogenization of a stationary mean-field game

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