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.

翻译：我们猜想PPAD类存在一个类似PCP的完全问题，其目标是寻找一个近似均衡状态，使得除极少数参与者外，绝大多数参与者的偏离动机都微乎其微。我们证明，若假设该问题需要指数时间求解，则该领域的若干开放问题将得以解决。通过"生日重复"归约法得到的最重要推论是：针对双人博弈纳什均衡的n^O(log n)近似方案[LMM03]本质上已达到最优。基于该猜想还可解决该领域另外两个开放问题，证明特定近似均衡属于PPAD完全问题：寻找双人纳什均衡的相对近似解（不含[Das13]提出的良支撑限制），以及求解具有微小清算误差且基尼系数接近最优的近似竞争均衡[Bud11]。