A seller wants to sell an item to $n$ buyers. The buyer valuations are drawn i.i.d. from a distribution, but the seller does not know this distribution; the seller only knows the support $[a,b]$. To be robust against the lack of knowledge of the environment and buyers' behavior, the seller optimizes over DSIC mechanisms, and measures the worst-case performance relative to an oracle with complete knowledge of buyers' valuations. Our analysis encompasses both the regret and the ratio objectives. For these objectives, we derive an optimal mechanism in closed form as a function of the support and the number of buyers $n$. Our analysis reveals three regimes of support information and a new class of robust mechanisms. i.) With "low" support information, the optimal mechanism is a second-price auction (SPA) with a random reserve, a focal class in the earlier literature. ii.) With "high" support information, we show that second-price auctions are strictly suboptimal, and an optimal mechanism belongs to a novel class of mechanisms we introduce, which we call $\textbf{pooling auctions}$ (POOL); whenever the highest value is above a threshold, the mechanism still allocates to the highest bidder, but otherwise the mechanism allocates to a uniformly random buyer, i.e., pools low types. iii.) With "moderate" support information, a randomization between SPA and POOL is optimal. We also characterize optimal mechanisms within nested central subclasses of mechanisms: standard mechanisms (only allocate to the highest bidder), SPA with random reserve, and SPA with no reserve. We show strict separations across classes, implying that deviating from standard mechanisms is necessary for robustness. Lastly, we show that the same results hold under other distribution classes that capture "positive dependence" (mixture of i.i.d., exchangeable and affiliated), as well as i.i.d. regular distributions.

翻译：一位卖家希望向$n$个买家出售一件物品。买家估值独立同分布于某个分布，但卖家未知该分布，仅知其支撑区间$[a,b]$。为对抗环境未知性与买家行为的不确定性，卖家优化DSIC机制，并以完全知晓买家估值的预言机为基准衡量最坏情形性能。我们的分析涵盖遗憾与比值两类目标。针对这些目标，我们推导出以支撑信息和买家数量$n$为参数的闭式最优机制。分析揭示了支撑信息的三个区间及一类新型鲁棒机制：i.) 在“低”支撑信息下，最优机制为带随机保留价的第二价格拍卖（SPA），这是早期文献的焦点类别；ii.) 在“高”支撑信息下，我们证明第二价格拍卖严格次优，最优机制属于我们引入的新型机制——**池化拍卖**（POOL）：当最高估值高于阈值时仍将物品分配给最高出价者，否则分配给均匀随机买家（即对低类型进行池化）；iii.) 在“中等”支撑信息下，SPA与POOL的随机化组合达到最优。我们还刻画了嵌套机制子类（仅分配给出价最高者的标准机制、带随机保留价的SPA、无保留价SPA）中的最优机制。各子类间的严格分离表明，偏离标准机制是实现鲁棒性的必要条件。最后，我们证明在捕获“正相依性”的其他分布类（独立同分布混合、可交换分布、关联分布）及独立同分布正则分布下，上述结论同样成立。