The celebrated model of auctions with interdependent valuations, introduced by Milgrom and Weber in 1982, has been studied almost exclusively under private signals $s_1, \ldots, s_n$ of the $n$ bidders and public valuation functions $v_i(s_1, \ldots, s_n)$. Recent work in TCS has shown that this setting admits a constant approximation to the optimal social welfare if the valuations satisfy a natural property called submodularity over signals (SOS). More recently, Eden et al. (2022) have extended the analysis of interdependent valuations to include settings with private signals and private valuations, and established $O(\log^2 n)$-approximation for SOS valuations. In this paper we show that this setting admits a constant factor approximation, settling the open question raised by Eden et al. (2022).

翻译：由米尔格罗姆和韦伯于1982年引入的经典相依估值拍卖模型，几乎完全是在私有信号$s_1,\ldots,s_n$（面向$n个竞拍者）和公共估值函数$v_i(s_1,\ldots,s_n)$的设定下研究的。理论计算机科学领域近期研究表明，若估值满足被称为信号下的子模性（SOS）的自然性质，则该设定可实现对最优社会福利的常数近似。更近一步，Eden等人（2022）将相依估值的分析扩展至包含私有信号和私有估值的场景，并针对SOS估值建立了$O(\log^2 n)$-近似。本文证明该设定可达到常数因子近似，从而解决了Eden等人（2022）提出的开放性问题。