Local well-posedness of general mean field game master equations

Chenchen Mou; Jianfeng Zhang; Jianjun Zhou

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arXiv · 2606.29132

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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Chenchen Mou, Jianfeng Zhang, Jianjun Zhou. 2026-06-28. Local well-posedness of general mean field game master equations. https://arxiv.org/abs/2606.29132

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