This paper considers prior-independent mechanism design, in which a single mechanism is designed to achieve approximately optimal performance on every prior distribution from a given class. Most results in this literature focus on mechanisms with truthtelling equilibria, a.k.a., truthful mechanisms. Feng and Hartline (2018) introduce the revelation gap to quantify the loss of the restriction to truthful mechanisms. We solve a main open question left in Feng and Hartline (2018); namely, we identify a non-trivial revelation gap for revenue maximization. Our analysis focuses on the canonical problem of selling a single item to a single agent with only access to a single sample from the agent's valuation distribution. We identify the sample-bid mechanism (a simple non-truthful mechanism) and upper-bound its prior-independent approximation ratio by 1.835 (resp. 1.296) for regular (resp. MHR) distributions. We further prove that no truthful mechanism can achieve prior-independent approximation ratio better than 1.957 (resp. 1.543) for regular (resp. MHR) distributions. Thus, a non-trivial revelation gap is shown as the sample-bid mechanism outperforms the optimal prior-independent truthful mechanism. On the hardness side, we prove that no (possibly non-truthful) mechanism can achieve prior-independent approximation ratio better than 1.073 even for uniform distributions.

中文翻译：

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样本定价的启示差距

本文考虑了先验无关机制的设计，其中设计了一种机制来在给定类的每个先验分布上实现近似最佳的性能。该文献中的大多数结果都集中在具有真言表达平衡的机制上，也就是真实机制。冯和哈特琳（Feng and Hartline，2018）引入了启示缺口，以量化对真实机制的限制所造成的损失。我们解决了Feng和Hartline（2018）中剩下的一个主要开放性问题; 也就是说，我们确定了一个不小的披露差距，以实现收益最大化。我们的分析着重于将单个项目出售给单个代理商而只能从代理商的估值分布中访问单个样本的典型问题。我们确定样本出价机制（一种简单的非真实机制），并针对规则（MHR）分布将其先验独立逼近率上限提高了1.835（1.296）。我们进一步证明，对于正态分布（MHR），没有任何一种真实的机制能获得优于1.957（相对于1.543）的先验独立逼近比。因此，显示了一个非平凡的披露差距，因为样本出价机制优于最佳的事前无关真实机制。在硬度方面，我们证明即使对于均匀分布，也没有任何机制（可能是非真实的）无法实现优于1.073的先验无关近似值。543）（定期（分别为MHR）分发）。因此，显示了一个非平凡的披露差距，因为样本出价机制优于最佳的事前无关真实机制。在硬度方面，我们证明即使均匀分布，也没有机制（可能是非真实的）无法实现优于1.073的先验无关近似值。543）（定期（分别为MHR）分发）。因此，显示了一个非平凡的披露差距，因为样本出价机制优于最佳的事前无关真实机制。在硬度方面，我们证明即使均匀分布，也没有机制（可能是非真实的）无法实现优于1.073的先验无关近似值。