We present a computational formulation for the approximate version of several variational inequality problems, investigating their computational complexity and establishing PPAD-completeness. Examining applications in computational game theory, we specifically focus on two key concepts: resilient Nash equilibrium, and multi-leader-follower games -- domains traditionally known for the absence of general solutions. In the presence of standard assumptions and relaxation techniques, we formulate problem versions for such games that are expressible in terms of variational inequalities, ultimately leading to proofs of PPAD-completeness.

翻译：我们提出了若干变分不等式问题近似版本的计算表述，研究了它们的计算复杂性并确立了PPAD完备性。通过考察计算博弈论中的应用，我们特别聚焦于两个核心概念：弹性纳什均衡与多领导者-追随者博弈——这两个传统上被认为缺乏通用解法的领域。在标准假设与松弛技术条件下，我们为此类博弈构建了可表述为变分不等式的问题版本，最终完成了PPAD完备性的证明。