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Mean field games with common noise and degenerate idiosyncratic noise

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arxiv 2207.10209 v2 pith:M2DYMMHI submitted 2022-07-20 math.AP math.PR

Pierre Cardaliaguet , Benjamin Seeger , Panagiotis Souganidis This is my paper · ORCID
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keywords noisefieldidiosyncraticmeansolutionssystemcommondegenerate
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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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Cited by 1 Pith paper

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  1. A study of common noise in mean field games

    math.AP 2024-12 conditional novelty 6.0 of 10

    The paper proves global well-posedness of mean field games master equations with an endogenous common noise variable under flat or L2/displacement monotonicity conditions, including in the presence of additive common noise.

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