几乎所有人都能几乎满意吗？PPAD的PCP特性与纳什均衡的不可近似性
Can Almost Everybody be Almost Happy? PCP for PPAD and the Inapproximability of Nash
AI总结：
该研究提出PPAD存在类PCP完全问题的猜想，证明若该问题需指数时间求解，可解决领域内多个开放问题，包括验证双人纳什均衡n^O(log n)近似方案的最优性，证明两类近似均衡问题为PPAD完全。
摘要：
我们提出猜想：PPAD存在一个类PCP的完全问题，该问题旨在寻找一种近似均衡，其中除极少数参与者外，其余所有参与者的偏离动机都极小。我们证明，若假设该问题需要指数时间求解，该领域内的若干开放问题将得到解决。其中最重要的推论通过“生日重复”归约证明：[LMM03]提出的针对双人博弈纳什均衡的n^O(log n)近似方案本质上是最优的。假设该猜想成立后，该领域另外两个开放问题也得以解决，即以下两类近似均衡问题被证明是PPAD完全的：寻找双人纳什均衡的相对近似（不要求[Das13]中的良支撑限制），以及具有小清算误差和近似最优基尼系数的等收入近似竞争均衡[Bud11]。
英文摘要：
We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this problem requires exponential time, several open problems in this area are settled. The most important implication, proved via a "birthday repetition" reduction, is that the n^O(log n) approximation scheme of [LMM03] for the Nash equilibrium of two-player games is essentially optimum. Two other open problems in the area are resolved once one assumes this conjecture, establishing that certain approximate equilibria are PPAD-complete: Finding a relative approximation of two-player Nash equilibria (without the well-supported restriction of [Das13]), and an approximate competitive equilibrium with equal incomes [Bud11] with small clearing error and near-optimal Gini coefficient.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
