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arXiv · 2207.10209

Mean field games with common noise and degenerate idiosyncratic noise

Pierre Cardaliaguet·Benjamin Seeger·Panagiotis Souganidis
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Abstract

We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilistically weak solutions of the mean field game system.

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Pierre Cardaliaguet, Benjamin Seeger, Panagiotis Souganidis. 2022-07-20. Mean field games with common noise and degenerate idiosyncratic noise. https://arxiv.org/abs/2207.10209

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