论文标题
在决策不确定性下的Nash-Stackelberg-Nash游戏中：模型和平衡
On Nash-Stackelberg-Nash Games under Decision-Dependent Uncertainties: Model and Equilibrium
论文作者
论文摘要
在本文中，我们与多个领导者和追随者讨论了两阶段的分层游戏类别，这称为Nash-Stackelberg-Nash（N-S-N）游戏。特别是，我们考虑在决策不确定性（DDU）下考虑N-S-N游戏。 DDU是指受决策者策略影响的不确定性，并且在游戏均衡分析中很少解决。在本文中，我们首先用完全无知的DDU制定N-S-N游戏，其中玩家与DDU之间的交互的特征是不确定性集，这些不确定性取决于玩家的策略。然后，通过巩固广义的纳什平衡和帕累托 - 纳什平衡来确定游戏平衡的严格定义。之后，我们通过应用Kakutani的固定点定理证明了DDU下N-S-N游戏的平衡。最后，提供了一个说明性的示例，以显示DDU对N-S-N游戏均衡的影响。
In this paper, we discuss a class of two-stage hierarchical games with multiple leaders and followers, which is called Nash-Stackelberg-Nash (N-S-N) games. Particularly, we consider N-S-N games under decision-dependent uncertainties (DDUs). DDUs refer to the uncertainties that are affected by the strategies of decision-makers and have been rarely addressed in game equilibrium analysis. In this paper, we first formulate the N-S-N games with DDUs of complete ignorance, where the interactions between the players and DDUs are characterized by uncertainty sets that depend parametrically on the players' strategies. Then, a rigorous definition for the equilibrium of the game is established by consolidating generalized Nash equilibrium and Pareto-Nash equilibrium. Afterward, we prove the existence of the equilibrium of N-S-N games under DDUs by applying Kakutani's fixed-point theorem. Finally, an illustrative example is provided to show the impact of DDUs on the equilibrium of N-S-N games.
