| Abstract: |
| There have been many serious studies on mean field game master equations in the literature. It is well known that the a priori Lipschitz estimates of solutions to master equations with respect to the probability measure variable are essentially necessary for their global well-posedness. The Lasry-Lions monotonicity, displacement monotonicity and anti-monotonicity conditions are found to be sufficient conditions to these Lipschitz estimates. However, whether these monotonicity conditions are necessary is unknown. In this talk, an essentially necessary and sufficient condition to these a priori Lipschitz estimates will be discussed and a unified approach to uniquely solve master equations will be established. The talk is based on a joint work with Jianfeng Zhang and Jianjun Zhou. |
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