A Class of Stochastic Games and Moving Free Boundary Problems
A Class of Stochastic Games and Moving Free Boundary Problems
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DOI：
10.1137/20m1322558
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Xin Guo;Wenpin Tang;Renyuan Xu
中科院分区：
文献类型：
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作者：
Xin Guo;Wenpin Tang;Renyuan Xu
在本文中，我们提出并分析了一类随机$N$-玩家游戏，其中包括有限燃料随机游戏作为一种特殊情况。我们首先推导出纳什均衡（NE）的充分条件的形式验证定理，这揭示了一个重要的游戏组成部分，玩家之间的互动。它是内斯最优性条件的分析表示，在现有的随机博弈文献中基本上缺失。内斯的推导首先涉及解决多维自由边界问题，然后是Skorokhod问题，其中边界是“移动”的，因为它取决于系统的变化和其他参与者的控制策略。最后，我们重新制定NE战略的形式控制秩相关的随机微分方程。
In this paper we propose and analyze a class of stochastic $N$-player games that includes finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem, which reveals an essential game component regarding the interaction among players. It is an analytical representation of the conditional optimality condition for NEs, largely missing in the existing literature on stochastic games. The derivation of NEs involves first solving a multi-dimensional free boundary problem and then a Skorokhod problem, where the boundary is "moving" in that it depends on both the changes of the system and the control strategies of other players. Finally, we reformulate NE strategies in the form of controlled rank-dependent stochastic differential equations.