Communication Complexity of Combinatorial Auctions with Submodular Valuations

Abstract

Previous chapter Next chapter Full AccessProceedings Proceedings of the 2013 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Communication Complexity of Combinatorial Auctions with Submodular ValuationsShahar Dobzinski and Jan VondrákShahar Dobzinski and Jan Vondrákpp.1205 - 1215Chapter DOI:https://doi.org/10.1137/1.9781611973105.87PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract We prove the first communication complexity lower bound for constant-factor approximation of the submodular welfare problem. More precisely, we show that a -approximation (≃ 0.816) for welfare maximization in combinatorial auctions with submodular valuations would require exponential communication. We also show NP-hardness of -approximation in a computational model where each valuation is given explicitly by a table of constant size. Both results rule out better than (1 − )-approximations in every oracle model with a separate oracle for each player, such as the demand oracle model. Our main tool is a new construction of monotone submodular functions that we call multi-peak submodular functions. Roughly speaking, given a family of sets , we construct a monotone submodular function f with a high value f(S) for every set S ∊ (a “peak”), and a low value on every set that does not intersect significantly any set in . We also study two other related problems: max-min allocation (for which we also get hardness of -approximation, in both models), and combinatorial public projects (for which we prove hardness of -approximation in the communication model, and hardness of -approximation in the computational model, using constant size valuations). Previous chapter Next chapter RelatedDetails Published:2013ISBN:978-1-61197-251-1eISBN:978-1-61197-310-5 https://doi.org/10.1137/1.9781611973105Book Series Name:ProceedingsBook Code:PR143Book Pages:xix + 1915