SIAM Journal on Computing, Volume 49, Issue 5, Page 927-958, January 2020.
We consider a fundamental problem in microeconomics: selling a single item to a number of potential buyers, whose values are drawn from known independent and regular (not necessarily identical) distributions. There are four widely used and widely studied mechanisms in the literature: Myerson Auction (OPT), Sequential Posted-Pricing (SPM), Second-Price Auction with Anonymous Reserve (AR), and Anonymous Pricing (AP). OPT is revenue-optimal but complicated and also experiences several issues in practice such as fairness; AP is the simplest mechanism but also generates the lowest revenue among these four mechanisms; SPM and AR are of intermediate complexity and revenue. We explore revenue gaps among these mechanisms, each of which is defined as the largest ratio between revenues from a pair of mechanisms. We establish two tight bounds and one tighter bound: 1. SPM vs. AP: this ratio studies the power of discrimination in pricing schemes. We obtain the tight ratio of constant ${\cal{C}}^* \approx {2.62}$, closing the gap between $[\frac{e}{e - 1}, e]$ left before. 2. AR vs. AP: this ratio measures the relative power of auction scheme vs. pricing scheme, when no discrimination is allowed. We attain the tight ratio of $\frac{\pi^2}{6} \approx 1.64$, closing the previously known bounds $[\frac{e}{e - 1}, e]$. 3. OPT vs. AR: this ratio quantifies the power of discrimination in auction schemes and is previously known to be somewhere between [2, e]. The lower bound of 2 was conjectured to be tight by Hartline and Roughgarden [Proceedings of the 10th ACM Conference on Electronic Commerce, 2009, pp. 225--234] and Alaei et al. [Games Econom. Behav., 118 (2019), pp. 494--510]. We acquire a better lower bound of 2.15 and thus disprove this conjecture.

中文翻译：

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简单机制之间的收紧差距

SIAM计算杂志，第49卷，第5期，第927-958页，2020年1月。
我们认为微观经济学中的一个基本问题是：将一件商品卖给许多潜在的买家，这些买家的价值来自已知的独立和规则（不一定相同）的分布。文献中有四种广泛使用和研究广泛的机制：迈尔森拍卖（OPT），顺序后定价（SPM），带有匿名储备的第二价格拍卖（AR）和匿名定价（AP）。OPT是收益最佳的，但是很复杂，并且在实践中还遇到一些问题，例如公平性；AP是最简单的机制，但在这四种机制中产生的收益也最低。SPM和AR具有中等复杂性和收益。我们探索了这些机制之间的收入差距，每种差距都被定义为来自两种机制的收入之间的最大比例。我们建立了两个严格的界限和一个更严格的界限：1. SPM与AP：这个比率研究定价方案中歧视的力量。我们获得常数$ {\ cal {C}} ^ * \ approx {2.62} $的紧密比率，缩小了之前剩余的$ [\ frac {e} {e-1}，e] $之间的差距。2. AR与AP：在不允许歧视的情况下，此比率衡量拍卖方案与定价方案的相对能力。我们获得$ \ frac {\ pi ^ 2} {6} \约1.64 $的紧密比率，从而接近先前已知的边界$ [\ frac {e} {e-1}，e] $。3. OPT vs. AR：这个比率量化了拍卖方案中歧视的力量，并且以前知道在[2，e]之间。Hartline和Roughgarden [第十届ACM电子商务会议论文集，2009年，第225--234页]和Alaei等人推测2的下限是紧密的。[游戏经济人。行为 118（2019），494--510页]。我们获得了更好的2.15下界，因此证明了这一猜想。