Prophet Inequalities for Subadditive Combinatorial Auctions

Abstract: 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.