论文标题
平均野战游戏主方程，具有反对单调性条件
Mean Field Game Master Equations with Anti-monotonicity Conditions
论文作者
论文摘要
众所周知，从Lasry-Lions意义上讲，无论是在平均野外游戏主方程的全球范围良好，以及平均野战平衡的独特性和平均野外游戏系统的解决方案而言，单调性条件对全球范围良好而至关重要。在文献中，单调性条件始终沿固定方向采用。在本文中，我们提出了一种新型的单调性条件，以相反的方向称为抗单调性条件，并为具有不可分割的哈密顿人的平均野外游戏主方程式建立了全球范围的良好性。我们的抗单调性条件使我们的数据违反了Lasry-Lions单调性和位移单调性条件。
It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and solutions to mean field game systems. In the literature, the monotonicity conditions are always taken in a fixed direction. In this paper we propose a new type of monotonicity condition in the opposite direction, which we call the anti-monotonicity condition, and establish the global well-posedness for mean field game master equations with nonseparable Hamiltonians. Our anti-monotonicity condition allows our data to violate both the Lasry-Lions monotonicity and the displacement monotonicity conditions.
