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From infinity to one: The reduction of some mean field games to a global control problem

Guéant, Olivier (2011), From infinity to one: The reduction of some mean field games to a global control problem. https://basepub.dauphine.fr/handle/123456789/7389

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Type
Document de travail / Working paper
Date
2011
Publisher
Université Paris-Dauphine
Series title
Cahiers de la Chaire Finance et Développement Durable
Series number
42
Published in
Paris
Pages
13
Metadata
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Author(s)
Guéant, Olivier
Abstract (EN)
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced in [11 , 12 , 13 ] and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation (see [14]), from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.
Subjects / Keywords
control problem; PDE; Mean field games theory
JEL
C72 - Noncooperative Games