Wellposedness of Mean Field Games with Common Noise under a Weak Monotonicity Condition
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Publication:3462516
DOI10.1137/140974730zbMATH Open1327.93403arXiv1406.7028OpenAlexW3105231990MaRDI QIDQ3462516
Author name not available (Why is that?)
Publication date: 15 January 2016
Published in: (Search for Journal in Brave)
Abstract: In this paper, we consider Mean Field Games in the presence of common noise relaxing the usual independence assumption of individual random noise. We assume a simple linear model with terminal cost satisfying a convexity and a weak monotonicity property. Our main result is showing existence and uniqueness of a Mean Field Game solution using the Stochastic Maximum Principle. The uniqueness is a result of a monotonicity property similar to that of Lasry and Lions. We use the Banach Fixed Point Theorem to establish an existence over small time duration and show that it can be extended over an arbitrary finite time duration.
Full work available at URL: https://arxiv.org/abs/1406.7028
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