论文标题
离散时间stackelberg的主方程与多个领导者平均野外游戏
Master equation of discrete-time Stackelberg mean field games with multiple leaders
论文作者
论文摘要
在本文中，我们考虑了一个离散时间的Stackelberg平均野外游戏，其中有限的领导者，有限的主要追随者和无限的次要追随者。领导者和追随者每个人都私下观察类型，这些类型是有条件地独立控制的马尔可夫过程。领导者是“ Stackelberg”的，这意味着他们致力于动态政策。我们考虑两种类型的追随者：专业和小型，每种都有私人类型。所有追随者都最好地回应Stackelberg领导人和彼此的政策。知道追随者将根据其政策进行卑鄙的野外游戏（与主要参与者）时，每个人（Stackelberg）领导者选择了一项最大化她奖励的政策。我们将结果结果称为具有多个领导者（SMFE-ML）的Stackelberg平均场平衡。在本文中，我们提供了该游戏的主方程式，该方程允许一个人计算所有SMFE-ML。当有无限人数的领导者人数时，我们将此概念进一步扩展到案例。
In this paper, we consider a discrete-time Stackelberg mean field game with a finite number of leaders, a finite number of major followers and an infinite number of minor followers. The leaders and the followers each observe types privately that evolve as conditionally independent controlled Markov processes. The leaders are of "Stackelberg" kind which means they commit to a dynamic policy. We consider two types of followers: major and minor, each with a private type. All the followers best respond to the policies of the Stackelberg leaders and each other. Knowing that the followers would play a mean field game (with major players) based on their policy, each (Stackelberg) leader chooses a policy that maximizes her reward. We refer to the resulting outcome as a Stackelberg mean field equilibrium with multiple leaders (SMFE-ML). In this paper, we provide a master equation of this game that allows one to compute all SMFE-ML. We further extend this notion to the case when there are infinite number of leaders.
