On the Equilibrium of a Class of Leader-Follower Games with Decision-Dependent Chance Constraints
<|reference_start|>On the Equilibrium of a Class of Leader-Follower Games with Decision-Dependent Chance Constraints: 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.<|reference_end|>
@article{wang2024on,
    title={On the Equilibrium of a Class of Leader-Follower Games with
  Decision-Dependent Chance Constraints},
    author={Jingxiang Wang, Zhaojian Wang, Bo Yang, Feng Liu, and Xinping Guan},
    journal={arXiv preprint arXiv:2408.02174},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.02174},
    primaryClass={math.OC cs.GT}
}