In this paper, we study the existence of equilibrium in a single-leader-multiple-follower game with decision-dependent chance constraints (DDCCs), where decision-dependent uncertainties (DDUs) exist in the constraints of followers. DDUs refer to the uncertainties impacted by the leader's strategy, while the leader cannot capture their exact probability distributions. To address such problems, we first use decision-dependent ambiguity sets under moment information and Cantelli's inequality to transform DDCCs into second-order cone constraints. This simplifies the game model by eliminating the probability distributions. We further prove that there exists at least one equilibrium point for this game by applying Kakutani's fixed-point theorem. Finally, a numerical example is provided to show the impact of DDUs on the equilibrium of such game models.

翻译：本文研究了一类具有决策依赖机会约束的单领导者-多追随者博弈的均衡存在性问题，其中追随者的约束条件存在决策依赖性不确定性。决策依赖性不确定性指受领导者策略影响的不确定性，而领导者无法获取其精确概率分布。针对此类问题，我们首先利用矩信息下的决策依赖模糊集与坎特利不等式，将决策依赖机会约束转化为二阶锥约束，从而通过消除概率分布简化了博弈模型。进一步应用角谷不动点定理，证明了该博弈至少存在一个均衡点。最后通过数值算例展示了决策依赖性不确定性对此类博弈模型均衡的影响。