AI 中文总结
该研究针对先验无关拍卖设计，证明无保留第二价格拍卖是$n\ge2$单调风险率竞拍者的极大极小最优机制，发现非标准机制比标准混合机制收益更高，揭示尾部约束对拍卖设计的影响。
AI 中文摘要
我们研究先验无关的拍卖设计，当竞拍者价值为独立同分布时，卖家仅知晓其分布的尺度不变形状约束，而既不知道分布也不知道价值的尺度。我们证明，在一大类占优策略激励相容机制上的极大极小问题可无损地简化为无尺度机制。对于任意$n\ge 2$个具有单调风险率的竞拍者，无保留的第二价格拍卖是该类机制（包括可能分配给较低出价者的随机机制）中的极大极小最优机制。我们推导了其针对每个$n$的精确保证，以及其相对于贝叶斯最优机制的损失消失的尖锐指数速率。许多熟悉的拍卖是标准的：它们仅将物品分配给出价最高的竞拍者，尽管激励相容并不要求如此。对于两个常规竞拍者，我们精确求解了标准问题：其最优机制将第二价格拍卖与相对加价拍卖混合，实现了约0.524413的最坏情况比率。我们构造了一种非标准机制，其有时将物品分配给出价较低的竞拍者，实现了约0.524829的比率，证明标准性具有严格的成本。这种对比由尾部约束驱动：单调风险率使得低排名分配无帮助，而常规性则允许其提高最坏情况收益。
英文摘要
We study prior-independent auction design when bidder values are independently and identically distributed and the seller knows only a scale-invariant shape restriction on their distribution, but neither the distribution nor the scale of values. We show that the maximin problem over a broad class of dominant-strategy incentive-compatible mechanisms reduces without loss to scale-free mechanisms. For any $n\ge 2$ monotone-hazard-rate bidders, the second-price auction without a reserve is maximin optimal over this class, including randomized mechanisms that may allocate to a lower bidder. We derive its exact guarantee for every $n$ and the sharp exponential rate at which its loss relative to the Bayesian optimum vanishes. Many familiar auctions are standard: they allocate only to a highest bidder, although incentive compatibility does not require this. For two regular bidders, we solve the standard problem exactly: its optimal mechanism mixes the second-price auction with a relative-markup auction and achieves a worst-case ratio of approximately $0.524413$. We construct a nonstandard mechanism that sometimes allocates to the lower bidder and achieves approximately $0.524829$, proving that standardness is strictly costly. The contrast is driven by tail restrictions: monotone hazard rate makes lower-rank allocation unhelpful, whereas regularity permits it to improve worst-case revenue.
