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

58 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

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10.1007/s13235-016-0203-5

Cite this

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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.",

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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.

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KW - Monotone schemes

KW - Numerical methods

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Two Numerical Approaches to Stationary Mean-Field Games

Abstract

Keywords

ASJC Scopus subject areas

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