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
M3 - منشور من مؤتمر
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 -