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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2021

Finite state Mean Field Games with Wright-Fisher common noise

Alekos Cecchin
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Asaf Cohen
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Résumé

We force uniqueness in finite state mean field games by adding a Wright-Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on the simplex whose characteristics solve the stochastic forward-backward system associated with the mean field game; see Cardaliaguet et al. [10]. We show that this equation, which is a non-linear version of the Kimura type equation studied in Epstein and Mazzeo [28], has a unique smooth solution whenever the normal component of the drift at the boundary is strong enough. Among others, this requires a priori estimates of Holder type for the corresponding Kimura operator when the drift therein is merely continuous.
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Dates et versions

hal-02953518 , version 1 (13-02-2023)

Licence

Paternité - Pas d'utilisation commerciale

Identifiants

Citer

Erhan Bayraktar, Alekos Cecchin, Asaf Cohen, François Delarue. Finite state Mean Field Games with Wright-Fisher common noise. Journal de Mathématiques Pures et Appliquées, 2021, 147, pp.98-162. ⟨10.1016/j.matpur.2021.01.003⟩. ⟨hal-02953518⟩
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