论文标题
在一般贝叶斯方法下存在确定性双杆游戏的解决方案
Existence of solutions for deterministic bilevel games under a general Bayesian approach
论文作者
论文摘要
1996年，Mallozzi和Morgan [33]提出了一个新的Stackelberg游戏模型，我们在这里称为贝叶斯方法。领导者只有有关追随者如何在可能的多个最佳选择中选择反应的部分信息。该部分信息被建模为与决策的分布，即领导者所谓的信念。在这项工作中，我们将这种方法的设置正式化，以供多个领导者承认多个领导者，并提供了解决方案的新结果。我们特别关注线性二聚体问题的基本案例，该问题以前尚未研究过，并且由追随者反应集的维度的可能变化给出了哪个主要困难。我们解决这一难度的主要技术是基于我们称为矩形连续性的设置值图的更强连续性概念，并通过参数线性问题的解决方案集对此进行了验证。最后，我们提供了一些数值实验，以解决贝叶斯方法下的线性二聚体问题。
In 1996, Mallozzi and Morgan [33] proposed a new model for Stackelberg games which we refer here to as the Bayesian approach. The leader has only partial information about how followers select their reaction among possibly multiple optimal ones. This partial information is modeled as a decision-dependent distribution, the so-called belief of the leader. In this work, we formalize the setting of this approach for bilevel games admitting multiple leaders and we provide new results of existence of solutions. We pay particular attention to the fundamental case of linear bilevel problems, which has not been studied before, and which main difficulty is given by possible variations in the dimension of the reaction set of the follower. Our main technique to address this difficulty is based on a stronger notion of continuity for set-valued maps that we call rectangular continuity, and which is verified by the solution set of parametric linear problems. Finally, we provide some numerical experiments to address linear bilevel problems under the Bayesian approach.
