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Local well-posedness of general mean field game master equations

  • Chenchen Mou
  • Jianfeng Zhang
  • Jianjun Zhou
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Abstract

This paper presents a generic approach for establishing mean field game master equations, applicable whenever the mean field equilibrium can be characterized by a McKean-Vlasov forward-backward stochastic differential equation system. The core of our approach is a representation formula for the first-order Lions derivative of the decoupling field of this forward-backward SDE system. We then employ a bootstrap argument to recursively compute its higher-order derivatives. To demonstrate the method's versatility, we establish the local well-posedness for master equations in three distinct models: extended mean field games, mean field games with volatility control, and mean field games with a major player.

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Cite

BibTeXRIS
BibTeX
@misc{mou2026local,
  title = {{Local well-posedness of general mean field game master equations}},
  author = {Chenchen Mou and Jianfeng Zhang and Jianjun Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.29132},
  eprint = {2606.29132},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.29132},
}
RIS
TY  - UNPB
TI  - Local well-posedness of general mean field game master equations
AU  - Chenchen Mou
AU  - Jianfeng Zhang
AU  - Jianjun Zhou
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2606.29132
UR  - https://arxiv.org/abs/2606.29132
AB  - This paper presents a generic approach for establishing mean field game master equations, applicable whenever the mean field equilibrium can be characterized by a McKean-Vlasov forward-backward stochastic differential equation system. The core of our approach is a representation formula for the first-order Lions derivative of the decoupling field of this forward-backward SDE system. We then employ a bootstrap argument to recursively compute its higher-order derivatives. To demonstrate the method's versatility, we establish the local well-posedness for master equations in three distinct models: extended mean field games, mean field games with volatility control, and mean field games with a major player.
ER  -