Breaking the logarithmic barrier for truthful combinatorial auctions with submodular bidders

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Abstract

We study a central problem in Algorithmic Mechanism Design: constructing truthful mechanisms for welfare maximization in combinatorial auctions with submodular bidders. Dobzinski, Nisan, and Schapira provided the first mechanism that guarantees a non-trivial approximation ratio of O(log2 m) [STOC'06], where m is the number of items. This was subsequently improved to an approximation factor of O(log mlog log m) [Dobzinski, APPROX'07] and then to O(log m) [Krysta and Vocking, ICALP'12]. In this paper we develop the first mechanism that breaks the logarithmic barrier. Specifically, the mechanism provides an approximation ratio of O(√log m). Similarly to previous constructions, our mechanism uses polynomially many value and demand queries, and in fact provides the same approximation ratio for the larger class of XOS (a.k.a.fractionally subadditive) valuations. We also develop a computationally efficient implementation of the mechanism for combinatorial auctions with budget additive bidders. Although in general computing a demand query is NP-hard for budget additive valuations, we observe that the specific form of demand queries that our mechanism uses can be efficiently computed when bidders are budget additive.

Original languageEnglish
Title of host publicationSTOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
EditorsYishay Mansour, Daniel Wichs
Pages940-948
Number of pages9
ISBN (Electronic)9781450341325
DOIs
StatePublished - 19 Jun 2016
Event48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States
Duration: 19 Jun 201621 Jun 2016

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
Volume19-21-June-2016

Conference

Conference48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016
Country/TerritoryUnited States
CityCambridge
Period19/06/1621/06/16

All Science Journal Classification (ASJC) codes

  • Software

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