Project

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Numerical methods for mean field games

Applicant Andreev Roman
Number 164616
Funding scheme Advanced Postdoc.Mobility
Research institution
Laboratoire Jacques-Louis Lions Université Paris Diderot
INRIA Unité de Recherche Rocquencourt Domaine de Voluceau
Institution of higher education Institution abroad - IACH
Main discipline Mathematics
Start/End 01.05.2016 - 31.08.2017
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All Disciplines (2)

Discipline
Mathematics
Information Technology

Keywords (5)

space-time discretization; compressive algorithms; mean field games; space-time preconditioning; algorithm based fault tolerance

Lay Summary (German)

Lead
Numerics for mean field games
Lay summary
In diesem Projekt betrachten wir die Gleichungen der sogennanten mean field games (MFGs). Die MFGs beschreiben Nash Gleichgewichte bei einer grossen Anzahl der Spieler, und finden somit soziale und ökonomische Anwendungen. In dem Projekt entwickeln wir numerische Methoden für die MFGs. Die Schwierigkeiten sind dabei etwa der möglicherweise hochdimensionale Zustandsraum, sowie die Nichtnegativitätsbedingung an die Verteilung der Spieler im Zustandsraum. Der hohe rechnerische Aufwand benötigt neue parallele Algorithmen. 
Direct link to Lay Summary Last update: 06.04.2016

Responsible applicant and co-applicants

Publications

Publication
Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion
Andreev Roman, Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion, in SIAM J. Sci. Comput., 0.

Collaboration

Group / person Country
Types of collaboration
CMAP, Ecole polytechnique France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
MOKAPLAN, INRIA Paris France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
ENSIMAG, Grenoble France (Europe)
- Industry/business/other use-inspired collaboration
Computational Mathematics, Chalmers / University of Gothenburg Sweden (Europe)
- Publication
TWT GmbH, Stuttgart Germany (Europe)
- Industry/business/other use-inspired collaboration
CLILLAC-ARP, Univ Paris Diderot France (Europe)
- in-depth/constructive exchanges on approaches, methods or results
ENS de Lyon France (Europe)
- Exchange of personnel

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Numerical Methods for Optimal Control and Inverse Problems Talk given at a conference On instationary mean field games with diffusion 05.04.2017 München, Germany Andreev Roman;
LJLL internal seminar Talk given at a conference Numerical methods for the 2nd moment of stochastic ODEs 16.11.2016 Paris, France Andreev Roman;
Mini-course (3x2h) Individual talk Space-time discretization and preconditioning of parabolic PDEs 08.06.2016 Göteborg, Sweden Andreev Roman;
Computational and Applied Mathematics (CAM) Seminar Individual talk Remarks on stochastic eigenvalues 01.06.2016 Göteborg, Sweden Andreev Roman;


Communication with the public

Communication Title Media Place Year
Other activities Busy bus | coding competition International 2017
Talks/events/exhibitions Vortrag an der Begabtenschule "Gusdorf" (Paris) International 2016

Use-inspired outputs

Abstract

Mean field games refer to a set of partial differential equations that were proposed by Lasry/Lions and Huang/Malhamé/Caines around 2006 to describe Nash equilibria for a continuum of agents who interact through their mean field. They have found applications such as (macro/micro)economic modeling, crowd motion, opinion dynamics, and vaccination, but also pose a range of new mathematical and numerical questions. Numerical methods for the mean field games equations are scarce. We will develop numerical methods for mean field games with massively parallel computer architectures in mind. We will investigate stable finite element discretizations and multilevel preconditioners in space-time, parallel scalability, space-time compressivity, and algorithm based fault tolerance.
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