TY - GEN

T1 - The menu-size complexity of revenue approximation

AU - Babaioff, Moshe

AU - Gonczarowski, Yannai A.

AU - Nisan, Noam

N1 - Publisher Copyright:
© 2017 Copyright held by the owner/author(s).

PY - 2017/6/19

Y1 - 2017/6/19

N2 - 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.

AB - 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.

KW - Approximate revenue maximization

KW - Auction

KW - Menu size

KW - Revenue maximization

UR - http://www.scopus.com/inward/record.url?scp=85024379374&partnerID=8YFLogxK

U2 - 10.1145/3055399.3055426

DO - 10.1145/3055399.3055426

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AN - SCOPUS:85024379374

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 869

EP - 877

BT - STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing

A2 - McKenzie, Pierre

A2 - King, Valerie

A2 - Hatami, Hamed

PB - Association for Computing Machinery

T2 - 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017

Y2 - 19 June 2017 through 23 June 2017

ER -