The menu-size complexity of revenue approximation

Moshe Babaioff, Yannai A. Gonczarowski*, Noam Nisan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Consider a monopolist selling n items to an additive buyer whose item values are drawn from independent distributions F1,F2,…,Fn possibly having unbounded support. Unlike in the single-item case, it is well known that the revenue-optimal selling mechanism (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. Also known is that simple mechanisms with a bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, whether an arbitrarily high fraction of the optimal revenue can be extracted via a bounded menu size remained open. We give an affirmative answer: for every n and ε>0, there exists C=C(n,ε) s.t. mechanisms of menu size at most C suffice for obtaining (1−ε) of the optimal revenue from any F1,…,Fn. We prove upper and lower bounds on the revenue-approximation complexity C(n,ε) and on the deterministic communication complexity required to run a mechanism achieving such an approximation.

Original languageAmerican English
Pages (from-to)281-307
Number of pages27
JournalGames and Economic Behavior
StatePublished - Jul 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.


  • Approximate revenue maximization
  • Auction
  • Communication complexity
  • Mechanism design
  • Menu size
  • Revenue maximization


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