论文标题
控制的平均野外游戏：单调性的传播
Mean Field Games of Controls: Propagation of Monotonicities
论文作者
论文摘要
平均野外游戏的理论认为，通过国家和控制的联合分布进行交互的一类平均野外游戏。众所周知，对于标准的平均野外游戏，某些单调性条件对于确保平均场平衡的独特性以及主人公的全球良好性至关重要。在文献中，单调性条件可能是Lasry-Lions单调性，位移单调性或抗单调性条件。在本文中，我们研究了所有这三种类型的单调性条件，用于均值控制措施的平均现场游戏，并沿着通用噪声的主方程式向主方程的解决方案展示它们的传播。特别是，我们将位移单调性扩展到了半单调性，即使对于标准平均野外游戏，其传播结果也是新的。这是迈向全球良好型理论的第一步，用于控制控制的平均野外游戏。
The theory of Mean Field Game of Controls considers a class of mean field games where the interaction is through the joint distribution of the state and control. It is well known that, for standard mean field games, certain monotonicity condition is crucial to guarantee the uniqueness of mean field equilibria and then the global wellposedness for master equations. In the literature, the monotonicity condition could be the Lasry-Lions monotonicity, the displacement monotonicity, or the anti-monotonicity conditions. In this paper, we investigate all these three types of monotonicity conditions for Mean Field Games of Controls and show their propagation along the solutions to the master equations with common noises. In particular, we extend the displacement monotonicity to semi-monotonicity, whose propagation result is new even for standard mean field games. This is the first step towards the global wellposedness theory for master equations of Mean Field Games of Controls.
