The menu-size complexity of revenue approximation

Moshe Babaioff, Yannai A. Gonczarowski, Noam Nisan

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

30 Scopus citations


We consider a monopolist that is selling n items to a single additive buyer, where the buyer's values for the items are drawn according to independent distributions F1, F2,⋯, Fn that possibly have unbounded support. It is well known that - unlike in the single item case - the revenue-optimal auction (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. It is also known that simple auctions with a finite bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, the question of the possibility of extracting an arbitrarily high fraction of the optimal revenue via a finite menu size remained open. In this paper, we give an affirmative answer to this open question, showing that for every n and for every ϵ > 0, there exists a complexity bound C = C(n, ϵ) such that auctions of menu size at most C suffice for obtaining a (1 - ϵ) fraction of the optimal revenue from any F1,⋯, Fn. We prove upper and lower bounds on the revenue approximation complexity C(n, ϵ), as well as on the deterministic communication complexity required to run an auction that achieves such an approximation.

Original languageAmerican English
Title of host publicationSTOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing
EditorsPierre McKenzie, Valerie King, Hamed Hatami
PublisherAssociation for Computing Machinery
Number of pages9
ISBN (Electronic)9781450345286
StatePublished - 19 Jun 2017
Event49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017 - Montreal, Canada
Duration: 19 Jun 201723 Jun 2017

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
VolumePart F128415
ISSN (Print)0737-8017


Conference49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017

Bibliographical note

Publisher Copyright:
© 2017 Copyright held by the owner/author(s).


  • Approximate revenue maximization
  • Auction
  • Menu size
  • Revenue maximization


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