论文标题
在平均野外游戏的逆边界问题上
On an inverse boundary problem for mean field games
论文作者
论文摘要
在本文中，我们提出并研究了由有限域中一阶主方程支配的平均野外游戏（MFG）的反向边界问题。我们通过证明在任何给定的（状态）时空子域中的运行成本函数是由该子域的MFG边界数据唯一确定的，我们建立了唯一的可识别性结果。我们的研究有几个显着特征。 MFG系统将两个非线性抛物线PDE与一个前进的时间融合在一起，另一个则在时间后退，此外还有一个概率度量约束。这些使逆问题研究是文献的新知识和高度挑战的。我们开发了一个有效的有效方案来解决反问题，包括非平凡分布周围概率空间的高阶变化，以及建立新型的CGO解决方案，以作为``探测模式''。我们的研究开辟了有关MFGS的反相反问题研究的新领域。
In this paper, we propose and study an inverse boundary problem for the mean field games (MFGs) governed by the first-order master equation in a bounded domain. We establish the unique identifiability result by showing that the running cost function within any given proper (state) space-time subdomain is uniquely determined by the MFG boundary data of this subdomain. There are several salient features of our study. The MFG system couples two nonlinear parabolic PDEs with one forward in time and the other one backward in time, and moreover there is a probability measure constraint. These make the inverse problem study new to the literature and highly challenging. We develop an effective and efficient scheme in tackling the inverse problem including the high-order variation in the probability space around a nontrivial distribution, and the construction of a novel class of CGO solutions to serve as the ``probing modes". Our study opens up a new field of research on inverse problems for MFGs.
