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A reference case for mean field games models

Guéant, Olivier (2009), A reference case for mean field games models, Journal de mathématiques pures et appliquées, 92, 3, p. 276-294. http://dx.doi.org/10.1016/j.matpur.2009.04.008

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Type
Article accepté pour publication ou publié
Date
2009
Journal name
Journal de mathématiques pures et appliquées
Volume
92
Number
3
Publisher
Elsevier
Pages
276-294
Publication identifier
http://dx.doi.org/10.1016/j.matpur.2009.04.008
Metadata
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Author(s)
Guéant, Olivier
Abstract (FR)
Nous présentons un exemple archétypal de jeu à champ moyen. Cet exemple est important à deux égards. Tout d'abord, il est suffisamment simple pour permettre l'obtention de solutions explicites : les fonctions de Bellman sont quadratiques, les mesures stationnaires gaussiennes et l'étude de la stabilité peut se faire explicitement en utilisant les polynômes d'Hermite. Aussi, et malgré la simplicité du problème, l'exemple que nous présentons est suffisamment riche pour être transposé mutatis mutandis à d'autres domaines d'application plus complexes.
Abstract (EN)
In this article, we present a reference case of mean field games. This case can be seen as a reference for two main reasons. First, the case is simple enough to allow for explicit resolution: Bellman functions are quadratic, stationary measures are normal and stability can be dealt with explicitly using Hermite polynomials. Second, in spite of its simplicity, the case is rich enough in terms of mathematics to be generalized and to inspire the study of more complex models that may not be as tractable as this one.
Subjects / Keywords
Partial differential equations; Mean field games; Control theory; Numerical methods
JEL
C65 - Miscellaneous Mathematical Tools
C62 - Existence and Stability Conditions of Equilibrium
C61 - Optimization Techniques; Programming Models; Dynamic Analysis
C73 - Stochastic and Dynamic Games; Evolutionary Games; Repeated Games

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