Prophet Secretary for Combinatorial Auctions and Matroids [chapter]

Soheil Ehsani, MohammadTaghi Hajiaghayi, Thomas Kesselheim, Sahil Singla
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most important of these generalizations are to matroids and to combinatorial auctions (extends bipartite matching). Kleinberg-Weinberg [KW12] and Feldman et al. [FGL15] show that for adversarial arrival order of random variables the optimal prophet inequalities
more » ... ve a 1/2-approximation. For many settings, however, it's conceivable that the arrival order is chosen uniformly at random, akin to the secretary problem. For such a random arrival model, we improve upon the 1/2-approximation and obtain (1 − 1/e)approximation prophet inequalities for both matroids and combinatorial auctions. This also gives improvements to the results of Yan [Yan11] and Esfandiari et al. [EHLM17] who worked in the special cases where we can fully control the arrival order or when there is only a single item. Our techniques are threshold based. We convert our discrete problem into a continuous setting and then give a generic template on how to dynamically adjust these thresholds to lower bound the expected total welfare.
doi:10.1137/1.9781611975031.46 dblp:conf/soda/EhsaniHKS18 fatcat:tgumcl4ftbhbpk575oywg5mtue