论文标题
离散时间Stackelberg的主方程与单个领导者平均野战游戏
Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader
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，具有领导者和无限的追随者。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。领导者承诺制定动态政策，追随者最能对该政策以及彼此做出回应。知道追随者将根据她的政策进行卑鄙的野外游戏，领导者选择了一项最大化她的奖励的政策。我们将结果的结果称为Stackelberg平均场平衡（SMFE）。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。根据我们的框架，我们考虑了两个数字示例。首先，我们考虑了一个流行病模型，其中关注者会根据平均野外人群感染。领导者选择了疫苗的补贴，以最大程度地提高社会福利并最大程度地减少疫苗接种成本。在第二个示例中，我们考虑了一个技术采用游戏，追随者决定采用技术或产品，而领导者决定了一种产品的成本，使他的收益最大化，这与采用该技术的人们成比例
In this paper, we consider a discrete-time Stackelberg mean field game with a leader and an infinite number of followers. The leader and the followers each observe types privately that evolve as conditionally independent controlled Markov processes. The leader commits to a dynamic policy and the followers best respond to that policy and each other. Knowing that the followers would play a mean field game based on her policy, the leader chooses a policy that maximizes her reward. We refer to the resulting outcome as a Stackelberg mean field equilibrium (SMFE). In this paper, we provide a master equation of this game that allows one to compute all SMFE. Based on our framework, we consider two numerical examples. First, we consider an epidemic model where the followers get infected based on the mean field population. The leader chooses subsidies for a vaccine to maximize social welfare and minimize vaccination costs. In the second example, we consider a technology adoption game where the followers decide to adopt a technology or a product and the leader decides the cost of one product that maximizes his returns, which are proportional to the people adopting that technology
