Finite state Mean Field Games with Wright-Fisher common noise
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. (2019). We show that this equation, which is a non-linear version of the Kimura type equation studied in Epstein and Mazzeo (2013), 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 H\"older type for the corresponding Kimura operator when the drift therein is merely continuous.
Keywords
Cite
@article{arxiv.1912.06701,
title = {Finite state Mean Field Games with Wright-Fisher common noise},
author = {Erhan Bayraktar and Alekos Cecchin and Asaf Cohen and Francois Delarue},
journal= {arXiv preprint arXiv:1912.06701},
year = {2021}
}