论文标题
线性编程虚拟播放算法，用于最佳停止和吸收的平均现场游戏
Linear Programming Fictitious Play algorithm for Mean Field Games with optimal stopping and absorption
论文作者
论文摘要
在线性编程方法的背景下，我们开发了虚拟的播放算法，用于具有常规控制和吸收的最佳停止和平均野外游戏的平均野外游戏。该算法允许通过解决与游戏中仍在游戏中的玩家的分布及其停止时间/控件相关的线性编程问题而无需计算值函数的平均现场游戏人群动态。我们使用衡量措施的汇聚拓扑拓扑来显示算法的收敛性，这是应对措施流缺乏连续性所需的。提供数值示例以说明算法的收敛性。
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean field game population dynamics without computing the value function by solving linear programming problems associated with the distributions of the players still in the game and their stopping times/controls. We show the convergence of the algorithm using the topology of convergence in measure in the space of subprobability measures, which is needed to deal with the lack of continuity of the flows of measures. Numerical examples are provided to illustrate the convergence of the algorithm.
