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
TypeDocument de travail / Working paper
Series titleCahiers de la Chaire Finance et Développement Durable
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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 ), 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 / Keywordscontrol problem; PDE; Mean field games theory
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Cannarsa, Piermarco; Capuani, Rossana; Cardaliaguet, Pierre (2021) Article accepté pour publication ou publié