In this paper, we revisit the problem of approximating a pacing equilibrium in second-price auctions, introduced by Conitzer, Kroer, Sodomka, and Moses [Oper. Res. 2022]. We show that finding a constant-factor approximation of a pacing equilibrium is PPAD-hard, thereby strengthening previous results of Chen, Kroer, and Kumar [Math. Oper. Res. 2024], which established PPAD-hardness only for inverse-polynomial approximations.

翻译：本文重新审视了由Conitzer、Kroer、Sodomka和Moses在《运筹学》2022年提出的次价拍卖中定价均衡的逼近问题。我们证明了寻找定价均衡的常数因子逼近是PPAD难的，从而强化了Chen、Kroer和Kumar在《数学运筹研究》2024年的先前结果——该结果仅确立了逆多项式逼近的PPAD难度。