Mean field games with singular controls

Guanxing Fu; Ulrich Horst

doi:10.1137/17M1123742

Mean field games with singular controls

Guanxing Fu
, Ulrich Horst

Department of Applied Mathematics

Research output: Journal article publication › Journal article › Academic research › peer-review

31 Citations (Scopus)

Abstract

This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of cadlag functions.

Original language	English
Pages (from-to)	3833-3868
Number of pages	36
Journal	SIAM Journal on Control and Optimization
Volume	55
Issue number	6
DOIs	https://doi.org/10.1137/17M1123742
Publication status	E-pub ahead of print - 30 Nov 2017

Keywords

Mean field game
Relaxed control
Singular control
Skorokhod M1 topology

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

More information

10.1137/17M1123742

Cite this

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title = "Mean field games with singular controls",

abstract = "This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of cadlag functions.",

keywords = "Mean field game, Relaxed control, Singular control, Skorokhod M1 topology",

author = "Guanxing Fu and Ulrich Horst",

note = "Funding Information: ∗Received by the editors March 31, 2017; accepted for publication (in revised form) September 20, 2017; published electronically November 30, 2017. http://www.siam.org/journals/sicon/55-6/M112374.html Funding: Financial support by the Berlin Mathematical School (BMS) and the SFB 649 Economic Risk is gratefully acknowledged. †Department of Mathematics, and Berlin Mathematical School, Humboldt-Universit{\"a}t zu Berlin Unter den Linden 6, 10099 Berlin, Germany ([email protected]). ‡Department of Mathematics, and School of Business and Economics, Humboldt-Universit{\"a}t zu Berlin Unter den Linden 6, 10099 Berlin, Germany ([email protected]). Publisher Copyright: {\textcopyright} 2017 Society for Industrial and Applied Mathematics.",

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AU - Horst, Ulrich

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N2 - This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of cadlag functions.

AB - This paper establishes the existence of relaxed solutions to mean field games (MFGs for short) with singular controls. We also prove approximations of solutions results for a particular class of MFGs with singular controls by solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of cadlag functions.

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KW - Relaxed control

KW - Singular control

KW - Skorokhod M1 topology

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DO - 10.1137/17M1123742

M3 - Journal article

AN - SCOPUS:85039934437

SN - 0363-0129

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EP - 3868

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 6

ER -

Mean field games with singular controls

Abstract

Keywords

ASJC Scopus subject areas

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