Two Numerical Approaches to Stationary Mean-Field Games

Noha Almulla; Rita Ferreira; Diogo Gomes

doi:10.1007/s13235-016-0203-5

Two Numerical Approaches to Stationary Mean-Field Games

Noha Almulla, Rita Ferreira, Diogo Gomes^*

^*Corresponding author for this work

Computer, Electrical and Mathematical Sciences and Engineering

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

55 Scopus citations

Abstract

Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

Original language	English (US)
Pages (from-to)	657-682
Number of pages	26
Journal	Dynamic Games and Applications
Volume	7
Issue number	4
DOIs	https://doi.org/10.1007/s13235-016-0203-5
State	Published - Dec 1 2017

Keywords

Mean-field games
Monotone schemes
Numerical methods

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Computer Science Applications
Computer Graphics and Computer-Aided Design
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

Access to Document

10.1007/s13235-016-0203-5

Cite this

@article{036c0339d627470bbc2b22791176fefd,

title = "Two Numerical Approaches to Stationary Mean-Field Games",

abstract = "Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.",

keywords = "Mean-field games, Monotone schemes, Numerical methods",

author = "Noha Almulla and Rita Ferreira and Diogo Gomes",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2017",

month = dec,

day = "1",

doi = "10.1007/s13235-016-0203-5",

language = "English (US)",

volume = "7",

pages = "657--682",

journal = "Dynamic Games and Applications",

issn = "2153-0785",

publisher = "Springer Verlag",

number = "4",

}

TY - JOUR

T1 - Two Numerical Approaches to Stationary Mean-Field Games

AU - Almulla, Noha

AU - Ferreira, Rita

AU - Gomes, Diogo

PY - 2017/12/1

Y1 - 2017/12/1

N2 - Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

AB - Here, we consider numerical methods for stationary mean-field games (MFG) and investigate two classes of algorithms. The first one is a gradient-flow method based on the variational characterization of certain MFG. The second one uses monotonicity properties of MFG. We illustrate our methods with various examples, including one-dimensional periodic MFG, congestion problems, and higher-dimensional models.

KW - Mean-field games

KW - Monotone schemes

KW - Numerical methods

UR - http://www.scopus.com/inward/record.url?scp=85029471535&partnerID=8YFLogxK

U2 - 10.1007/s13235-016-0203-5

DO - 10.1007/s13235-016-0203-5

M3 - Article

AN - SCOPUS:85029471535

SN - 2153-0785

VL - 7

SP - 657

EP - 682

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

IS - 4

ER -

Two Numerical Approaches to Stationary Mean-Field Games

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this