In practice, auction data are often endogenously censored and anonymous, revealing only limited outcome statistics rather than full bid profiles. We study robust auction design when the seller observes only aggregated, anonymous order statistics and seeks to maximize worst-case expected revenue over all product distributions consistent with the observed statistic. We show that simple and widely used mechanisms are robustly optimal. Specifically, posted pricing is robustly optimal given the distribution of the highest value; the Myerson auction designed for the unique consistent i.i.d. distribution is robustly optimal given the lowest value distribution; and the second-price auction with an optimal reserve is robustly optimal when an intermediate order statistic is observed and the implied i.i.d. distribution is regular above its reserve. More generally, for a broad class of monotone symmetric mechanisms depending only on the top k order statistics, including multi-unit and position auctions, the worst-case revenue is attained under the i.i.d. distribution consistent with the observed k-th order statistic. Our results provide a tractable foundation for non-discriminatory auction design, where fairness and privacy are intrinsic consequences of the information structure rather than imposed constraints.

翻译：实践中，拍卖数据往往是内生截断且匿名的，仅揭示有限的结果统计量而非完整的出价剖面。本文研究当卖方仅观测到聚合的匿名顺序统计量时，如何设计鲁棒拍卖机制，以在所有与观测统计量一致的价值分布中最大化最坏情况期望收益。我们证明，简单且广泛使用的机制具有鲁棒最优性。具体而言：给定最高价值分布时，固定价格机制具有鲁棒最优性；给定最低价值分布时，针对唯一一致独立同分布设计的Myerson拍卖具有鲁棒最优性；当观测到中间顺序统计量且隐含的独立同分布在保留价以上满足正则性时，带最优保留价的第二价格拍卖具有鲁棒最优性。更一般地，对于一大类仅依赖前k个顺序统计量的单调对称机制（包括多单位拍卖和位置拍卖），最坏情况收益可在与观测的第k个顺序统计量一致的独立同分布下达到。我们的结果为非歧视性拍卖设计提供了可处理的理论基础，其中公平性与隐私性成为信息结构的内在结果而非外部约束。