论文标题
在某些卑鄙的野外游戏和通过保护法的镜头上
On Some Mean Field Games and Master Equations through the lens of conservation laws
论文作者
论文摘要
在本手稿中，我们得出了一个在概率度量空间上编写的新的非线性传输方程，该方程允许研究一类确定性平均野外游戏和主方程，其中仅在终端时发生代理的相互作用。通过该传输方程式通过该传输方程式的观点有两个重要的后果。首先，该方程式揭示了一种新的单调性条件，这对于MFG NASH均衡的独特性和全球时间良好方程式都足够。有趣的是，这种情况通常是二分法的，迄今为止在文献中研究了Lasry-Lions和位移单调性条件。其次，在没有单调性的情况下，可以使用传输方程的保守形式来定义主方程的弱熵溶液。我们构建了几个具体示例，以证明MFG NASH均衡（无论它们是否实际存在）可能不会由主方程的熵解决方案选择。
In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens only at the terminal time. The point of view via this transport equation has two important consequences. First, this equation reveals a new monotonicity condition that is sufficient both for the uniqueness of MFG Nash equilibria and for the global in time well-posedness of master equations. Interestingly, this condition is in general in dichotomy with both the Lasry--Lions and displacement monotonicity conditions, studied so far in the literature. Second, in the absence of monotonicity, the conservative form of the transport equation can be used to define weak entropy solutions to the master equation. We construct several concrete examples to demonstrate that MFG Nash equilibria, whether or not they actually exist, may not be selected by the entropy solutions of the master equation.
