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 Hölder type for the corresponding Kimura operator when the drift therein is merely continuous.

Finite state mean field games with Wright–Fisher common noise

Cecchin A.;
2021

Abstract

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 Hölder type for the corresponding Kimura operator when the drift therein is merely continuous.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3442218
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