Finite state Mean Field Games with Wright-Fisher common noise
- Others:
- Department of Mathematics, University of Michigan ; Department of Mathematics, University of Michigan ; University of Michigan [Ann Arbor] ; University of Michigan System-University of Michigan System-University of Michigan [Ann Arbor] ; University of Michigan System-University of Michigan System
- Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
- ANR-19-P3IA-0002 - 3IA Côte d'Azur - Nice - Interdisciplinary Institute for Artificial Intelligence
- ANR-16-CE40-0015-01 - MFG - Mean Field Games
- ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019)
- ANR-16-CE40-0015,MFG,Jeux Champs Moyen(2016)
Description
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.
Abstract
International audience
Additional details
- URL
- https://hal.archives-ouvertes.fr/hal-02953518
- URN
- urn:oai:HAL:hal-02953518v1
- Origin repository
- UNICA