AI 中文总结
研究具有一个领导者和多个追随者的斯塔克尔伯格博弈，稳健领导者考虑最坏情况，通过弱形式将问题转化为零和博弈，利用HJB方程刻画，还指出委托代理问题是其特殊情况。
AI 中文摘要
本文研究了一个具有一个领导者和多个追随者的斯塔克尔伯格博弈。给定领导者的控制，追随者求解一个可能有多个均衡的纳什博弈。我们考虑一个稳健的领导者，他考虑最坏的情况，即追随者会选择对领导者最不利的均衡。通过使用弱形式，该问题诱导出一个具有开环控制的零和博弈问题，这是时间不一致的。我们将通过概率测度的瓦瑟斯坦空间上的HJB方程来刻画最后一个问题。一个委托人和多个代理人的委托代理问题可以看作是我们问题的一个特殊情况，但有一定的约束。
英文摘要
In this paper we study a Stackelberg game with one leader and multiple followers. Given the leader's control, the followers solve a Nash game with possibly multiple equilibria. We consider a robust leader who considers the worst scenario, namely the followers would select the equilibrium worst for the leader. By using the weak formulation, the problem induces a zero sum game problem with open loop controls, which is time inconsistent. We shall characterize the last problem through an HJB equation on the Wasserstein space of probability measures. The principal-agent problem with one principal and multiple agents can be viewed as a special case of our problem, but with certain constraints.
