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.

在本文中，我们讨论了一类具有多个领导者和追随者的两阶段分层博弈，称为 Nash-Stackelberg-Nash (N-S-N) 博弈。特别是，我们考虑了决策相关不确定性（DDU）下的 N-S-N 博弈。DDU 是指受决策者策略影响的不确定性，在博弈均衡分析中很少涉及。在本文中，我们首先制定了具有完全无知 DDU 的 N-S-N 博弈，其中参与者和 DDU 之间的交互的特征在于参数上取决于参与者策略的不确定性集。然后，通过合并广义纳什均衡和帕累托-纳什均衡，建立了博弈均衡的严格定义。之后，我们通过应用角谷不动点定理证明了 DDU 下 N-S-N 博弈均衡的存在。最后，提供了一个说明性示例来说明 DDU 对 N-S-N 博弈均衡的影响。