具有最优停止和吸收的平均场博弈的线性规划虚拟博弈算法

IF 1.9 3区 数学 Q2 Mathematics
Roxana Dumitrescu, Marcos Leutscher, P. Tankov
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引用次数: 8

摘要

在线性规划方法的背景下,我们开发了具有最优停止和具有规则控制和吸收的平均场博弈的虚拟博弈算法。该算法允许通过解决与仍在游戏中的玩家分布及其停止时间/控制相关的线性规划问题来计算价值函数,而无需计算平均场游戏人口动态。我们利用子概率测度空间中的测度收敛拓扑来证明算法的收敛性,这是处理测度流缺乏连续性所需要的。数值算例说明了该算法的收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Linear programming fictitious play algorithm for mean field games with optimal stopping and absorption
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.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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