Non-local Mean-Field Games: Existence

Diogo A. Gomes; Edgard A. Pimentel; Vardan Voskanyan

doi:10.1007/978-3-319-38934-9_10

Non-local Mean-Field Games: Existence

Diogo A. Gomes^*, Edgard A. Pimentel, Vardan Voskanyan

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

MFGs where the Hamilton–Jacobi equation depends on the distribution of players in a non-local way make up an important group of problems. In many examples, this dependence is given by regularizing convolution operators. We split the discussion of non-local problems into two cases. First, we consider first-order MFGs. Here, semiconcavity bounds and the optimal control characterization of the Hamilton–Jacobi equation are the main tools. Next, we examine second-order MFGs. Here, the regularizing effects of parabolic equations and the L² stability of the Fokker–Planck equation are the main ingredients of the proof.

Original language	English (US)
Title of host publication	SpringerBriefs in Mathematics
Publisher	Springer Science and Business Media B.V.
Pages	125-130
Number of pages	6
DOIs	https://doi.org/10.1007/978-3-319-38934-9_10
State	Published - 2016

Publication series

Name	SpringerBriefs in Mathematics
ISSN (Print)	2191-8198
ISSN (Electronic)	2191-8201

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing Switzerland.

Keywords

Borel Probability Measure
Jacobi Equation
Parabolic Equation
Planck Equation
Viscosity Solution

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-38934-9_10

Cite this

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abstract = "MFGs where the Hamilton–Jacobi equation depends on the distribution of players in a non-local way make up an important group of problems. In many examples, this dependence is given by regularizing convolution operators. We split the discussion of non-local problems into two cases. First, we consider first-order MFGs. Here, semiconcavity bounds and the optimal control characterization of the Hamilton–Jacobi equation are the main tools. Next, we examine second-order MFGs. Here, the regularizing effects of parabolic equations and the L2 stability of the Fokker–Planck equation are the main ingredients of the proof.",

keywords = "Borel Probability Measure, Jacobi Equation, Parabolic Equation, Planck Equation, Viscosity Solution",

author = "Gomes, {Diogo A.} and Pimentel, {Edgard A.} and Vardan Voskanyan",

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year = "2016",

doi = "10.1007/978-3-319-38934-9_10",

language = "English (US)",

series = "SpringerBriefs in Mathematics",

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T2 - Existence

AU - Gomes, Diogo A.

AU - Pimentel, Edgard A.

AU - Voskanyan, Vardan

PY - 2016

Y1 - 2016

N2 - MFGs where the Hamilton–Jacobi equation depends on the distribution of players in a non-local way make up an important group of problems. In many examples, this dependence is given by regularizing convolution operators. We split the discussion of non-local problems into two cases. First, we consider first-order MFGs. Here, semiconcavity bounds and the optimal control characterization of the Hamilton–Jacobi equation are the main tools. Next, we examine second-order MFGs. Here, the regularizing effects of parabolic equations and the L2 stability of the Fokker–Planck equation are the main ingredients of the proof.

AB - MFGs where the Hamilton–Jacobi equation depends on the distribution of players in a non-local way make up an important group of problems. In many examples, this dependence is given by regularizing convolution operators. We split the discussion of non-local problems into two cases. First, we consider first-order MFGs. Here, semiconcavity bounds and the optimal control characterization of the Hamilton–Jacobi equation are the main tools. Next, we examine second-order MFGs. Here, the regularizing effects of parabolic equations and the L2 stability of the Fokker–Planck equation are the main ingredients of the proof.

KW - Borel Probability Measure

KW - Jacobi Equation

KW - Parabolic Equation

KW - Planck Equation

KW - Viscosity Solution

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M3 - Chapter

AN - SCOPUS:85101055715

T3 - SpringerBriefs in Mathematics

SP - 125

EP - 130

BT - SpringerBriefs in Mathematics

PB - Springer Science and Business Media B.V.

ER -

Non-local Mean-Field Games: Existence

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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