In this paper, we survey literature on prophet inequalities for subadditive combinatorial auctions. We give an overview of the previous best $O(\log \log m)$ prophet inequality as well as the preceding $O(\log m)$ prophet inequality. Then, we provide the constructive posted price mechanisms used in order to prove the two bounds. We mainly focus on the most recent literature that resolves a central open problem in this area of discovering a constant factor prophet inequality for subadditive valuations. We detail the approach of this new paper, which is $\textit{non-constructive}$ and therefore cannot be implemented using prices, as done in previous literature.

翻译：本文综述了关于次可加组合拍卖中先知不等式的相关文献。我们概述了之前最优的 $O(\log \log m)$ 先知不等式以及更早的 $O(\log m)$ 先知不等式。随后，我们介绍了为证明这两个界而使用的构造性标价机制。重点聚焦于最新文献，该文献解决了该领域一个核心开放问题——发现了次可加估值下的常数因子先知不等式。我们详细阐述了这篇新论文的方法，该方法具有 $\textit{非构造性}$ 特征，因此无法像先前文献那样通过定价机制实现。