The Root of Revenue Continuity
Sergiu Hart and Noam Nisan
在销售一种或多种商品的设定中，已有各种论文以不同形式和目的表明，买家估值分布的微小变化可能只会导致可提取收入的微小变化。我们为此证明了一个简单、清晰、方便且通用的陈述：设X和Y为k种可加性商品的随机估值，W(X,Y)为它们之间的Wasserstein距离（或称"推土机距离"）；则有√Rev(X)-√Rev(Y) ≤ √W(X,Y)。这进一步意味着，对X的任何最优机制进行简单的显式修改（即"统一折扣"），可以保证对于任何在Wasserstein距离上与X接近的Y都几乎是最优的。
In the setup of selling one or more goods, various papers have shown, in various forms and for various purposes, that a small change in the distribution of a buyer's valuations may cause only a small change in the possible revenue that can be extracted. We prove a simple, clean, convenient, and general statement to this effect: let X and Y be random valuations on k additive goods, and let W(X,Y) be the Wasserstein (or "earth mover's") distance between them; then sqrt(Rev(X))-sqrt(Rev(Y)) <= sqrt...