Inapproximability for VCG-based combinatorial auctions

Dave Buchfuhrer*, Shaddin Dughmi, Hu Fu, Robert Kleinberg, Elchanan Mossel, Christos Papadimitriou, Michael Schapira, Yaron Singer, Chris Umans

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

43 Scopus citations


The existence of incentive-compatible, computationally-efficient mechanisms for combinatorial auctions with good approximation ratios is the paradigmatic problem in algorithmic mechanism design. It is believed that, in many cases, good approximations for combinatorial auctions may be unattainable due to an inherent clash between truthfulness and computational efficiency. In this paper, we prove the first computational-complexity inapproximability results for incentive-compatible mechanisms for combinatorial auctions. Our results are tight, hold for the important class of VCG-based mechanisms, and are based on the complexity assumption that NP has no polynomial-size circuits. We show two different techniques to obtain such lower bounds: one for deterministic mechanisms that attains optimal dependence on the number of players and number of items, and one that also applies to a class of randomized mechanisms and attains optimal dependence on the number of players. Both techniques are based on novel VC dimension machinery.

Original languageAmerican English
Title of host publicationProceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms
PublisherAssociation for Computing Machinery (ACM)
Number of pages19
ISBN (Print)9780898717013
StatePublished - 2010
Externally publishedYes
Event21st Annual ACM-SIAM Symposium on Discrete Algorithms - Austin, TX, United States
Duration: 17 Jan 201019 Jan 2010

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms


Conference21st Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CityAustin, TX


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