样本定价的启示差距
Revelation Gap for Pricing from Samples
摘要：
本文考虑先验独立的机制设计，其中一个单一的机制设计，以实现近似最优性能的每个先验分布从一个给定的类。这篇文献中的大多数结果都集中在具有真相平衡的机制上，真实的机制Feng和Hartline（2018）引入了启示差距来量化对真实机制的限制的损失。我们解决了Feng和Hartline（2018）中留下的一个主要开放问题;即，我们确定了收入最大化的非平凡的启示差距。我们的分析集中在一个典型的问题，销售一个单一的项目，只有一个单一的样本，从代理的估值分布的单一代理。我们确定了样本出价机制（一个简单的非真实机制），并将其先验独立近似比的上限定为1.835（分别为）。1.296）对于常规（分别为MHR）分布。我们进一步证明，没有真实的机制可以实现先验独立的近似比优于1.957（分别为。1.543）对于常规（分别为MHR）分布。因此，一个非平凡的启示差距显示为样本出价机制优于最佳的先验独立的真实机制。在硬度方面，我们证明了没有（可能是非真实的）机制可以实现优先独立的近似比优于1.073，即使均匀分布。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
