论文标题
具有共同噪音和相关McKean-Vlasov FBSDES的突出的平均野外游戏的强大解决方案
Strong solutions to submodular mean field games with common noise and related McKean-Vlasov FBSDEs
论文作者
论文摘要
本文研究了具有共同噪声的多维平均野外游戏和McKean-Vlasov向前返回的随机微分方程的相关系统，这些方程是从随机最大原理中得出的。我们首先提出了一些与基础平均野外游戏的次数相关的结构条件，并且是众所周知的Lasry-Lions单调性的一种相反版本。通过通过随机最大原则重新加以最小化的代表性玩家最小化问题，supdrodimulity条件允许证明前向后系统的比较原理，这与最佳答复图的单调性相对应。在此属性的基础上，通过Tarski的固定点定理显示了强大解决方案的存在，无论是在平均野外游戏和相关的McKean-Vlasov前向下系统中。在这两种情况下，一组解决方案都具有晶格结构，具有最小和最大的解决方案，可以通过迭代最佳答复图或通过虚拟的播放算法来构建。
This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some structural conditions which are related to the submodularity of the underlying mean field game and are a sort of opposite version of the well known Lasry-Lions monotonicity. By reformulating the representative player minimization problem via the stochastic maximum principle, the submodularity conditions allow to prove comparison principles for the forward-backward system, which correspond to the monotonicity of the best reply map. Building on this property, existence of strong solutions is shown via Tarski's fixed point theorem, both for the mean field game and for the related McKean-Vlasov forward-backward system. In both cases, the set of solutions enjoys a lattice structure, with minimal and maximal solutions which can be constructed by iterating the best reply map or via the fictitious play algorithm.
