论文标题
存在薄弱的解决方案的均值均值游戏
Existence of weak solutions to time-dependent mean-field games
论文作者
论文摘要
在这里，我们建立了薄弱的解决方案，以实现广泛的时间依赖时间的单调均值游戏（MFGS）。这些MFG作为具有初始和终端条件的退化抛物线方程的系统。为了构建这些解决方案，我们考虑了时空中的高阶椭圆正则化。然后，使用Schaefer的固定点定理，我们获得了此正规化问题的存在和唯一性。使用Minty的方法，我们证明了原始MFG的弱解决方案。最后，本文以讨论拥塞问题和密度约束的MFG结束。
Here, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct these solutions, we consider a high-order elliptic regularization in space-time. Then, using Schaefer's fixed-point theorem, we obtain the existence and uniqueness for this regularized problem. Using Minty's method, we prove the existence of a weak solution to the original MFG. Finally, the paper ends with a discussion on congestion problems and density constrained MFGs.
