Finite state mean field games with Wright-Fisher common noise
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Publication:2656180
DOI10.1016/J.MATPUR.2021.01.003zbMATH Open1459.91012arXiv1912.06701OpenAlexW3121688281MaRDI QIDQ2656180
Author name not available (Why is that?)
Publication date: 10 March 2021
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1912.06701
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