论文标题
拉格朗日分散差异平均现场游戏
Lagrangian discretization of variational mean field games
论文作者
论文摘要
在本文中，我们介绍了一种方法，以通过有限的玩家轨迹集近似于交通拥堵的某些变异平均野外游戏问题。这些轨迹是通过解决类似于初始变异问题的最小化问题来获得的。在这个离散的问题中，交通拥堵受到2-wasserstein距离的莫罗包裹的惩罚。使用半混凝土最佳运输对此包络以及其值和变化的有效计算。我们在某些条件下，在离散化参数的某些条件下，我们显示了离散轨迹集朝向均值游戏解决方案的融合。
In this article, we introduce a method to approximate solutions of some variational mean field game problems with congestion, by finite sets of player trajectories. These trajectories are obtained by solving a minimization problem similar to the initial variational problem. In this discretized problem, congestion is penalized by a Moreau envelop with the 2-Wasserstein distance. Study of this envelop as well as efficient computation of its values and variations is done using semi-discrete optimal transport. We show convergence of the discrete sets of trajectories toward a solution of the mean field game, under some conditions on the parameters of the discretization.
