research-article

The menu-size complexity of revenue approximation

Authors:

Moshe Babaioff,

Yannai A. Gonczarowski,

Noam NisanAuthors Info & Claims

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

Pages 869 - 877

https://doi.org/10.1145/3055399.3055426

Published: 19 June 2017 Publication History

Get Access

Abstract

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,…,F_n 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,…,F_n. 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.

Supplementary Material

MP4 File (d3_sb_t7.mp4)

Download
133.36 MB

References

[1]

Moshe Babaioff, Nicole Immorlica, Brendan Lucier, and S. Matthew Weinberg. 2014. A simple and approximately optimal mechanism for an additive buyer. In Proceedings of the IEEE 55th Annual Symposium on Foundations of Computer Science (FOCS). 21–30. Patrick Briest, Shuchi Chawla, Robert Kleinberg, and S. Matthew Weinberg. 2010.

Digital Library

Google Scholar

[2]

Pricing randomized allocations. In Proceedings of the Twenty-First Annual ACMSIAM Symposium on Discrete Algorithms (SODA). 585–597. Shuchi Chawla, David L. Malec, and Balasubramanian Sivan. 2010.

Digital Library

Google Scholar

[3]

How good are simple mechanisms for selling multiple goods? Discussion Paper 666. Center for the Study of Rationality, Hebrew University of Jerusalem. Sergiu Hart and Philip J. Reny. 2015. Maximal revenue with multiple goods: Nonmonotonicity and other observations. Theoretical Economics 10, 3 (2015), 893–922. Xinye Li and Andrew Chi-Chih Yao. 2013.

Crossref

Google Scholar

[4]

On revenue maximization for selling multiple independently distributed items. Proceedings of the National Academy of Sciences (PNAS) 110, 28 (2013), 11232–11237.

Google Scholar

[5]

Alejandro M. Manelli and Daniel R. Vincent. 2006.

Google Scholar

Cited By

View all

Alaei SChawla SMakhdoumi AMalekian A(2023)Countering Value Uncertainty via Refunds: A Mechanism Design ApproachSSRN Electronic Journal10.2139/ssrn.4561235Online publication date: 2023
https://doi.org/10.2139/ssrn.4561235
Balseiro SDeng YMao JMirrokni VZuo S(2023)Optimal Mechanisms for a Value Maximizer: The Futility of Screening TargetsSSRN Electronic Journal10.2139/ssrn.4351927Online publication date: 2023
https://doi.org/10.2139/ssrn.4351927
Assadi SKher VLi GSchvartzman ALeyton-Brown KSamuelson LHartline J(2023)Fine-Grained Buy-Many Mechanisms Are Not Much Better Than BundlingProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597662(123-152)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597662
Show More Cited By

Index Terms

The menu-size complexity of revenue approximation
1. Theory of computation
  1. Computational complexity and cryptography
    1. Communication complexity
  2. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design

Recommendations

Bounding the menu-size of approximately optimal auctions via optimal-transport duality
STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing

The question of the minimum menu-size for approximate (i.e., up-to-ε) Bayesian revenue maximization when selling two goods to an additive risk-neutral quasilinear buyer was introduced by Hart and Nisan [2013], who give an upper bound of O(1/ε⁴) for this ...
Mixed-bundling auctions with reserve prices
AAMAS '12: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2

Revenue maximization in multi-item settings is notoriously elusive. This paper studies a class of two-item auctions which we call a mixed-bundling auction with reserve prices (MBARP). It calls VCG on an enlarged set of agents by adding the seller---who ...
On Envy-Free Revenue Approximation for Combinatorial Buyers with Budgets
Abstract
We study the computation of revenue-maximizing envy-free outcomes, in a monopoly market with budgeted buyers. Departing from previous works, we focus on buyers with combinatorial valuation functions, that are defined over subsets of distinct ...

Comments

Information & Contributors

Information

Published In

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

June 2017

1268 pages

ISBN:9781450345286

DOI:10.1145/3055399

General Chairs:
Hamed Hatami
McGill University
,
Pierre McKenzie
Université de Montréal
,
Program Chair:
Valerie King
University of Victoria

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 June 2017

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

European Research Council
Israel Science Foundation
Israel Academy of Sciences and Humanities
United States-Israel Binational Science Foundation

Conference

STOC '17

Sponsor:

SIGACT

STOC '17: Symposium on Theory of Computing

June 19 - 23, 2017

Montreal, Canada

Acceptance Rates

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

Upcoming Conference

STOC '25

Sponsor:
sigact

57th Annual ACM Symposium on Theory of Computing (STOC 2025)

June 23 - 27, 2025

Prague , Czech Republic

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

22
Total Citations
View Citations
112
Total Downloads

Downloads (Last 12 months)20
Downloads (Last 6 weeks)1

Reflects downloads up to 03 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

View all

Alaei SChawla SMakhdoumi AMalekian A(2023)Countering Value Uncertainty via Refunds: A Mechanism Design ApproachSSRN Electronic Journal10.2139/ssrn.4561235Online publication date: 2023
https://doi.org/10.2139/ssrn.4561235
Balseiro SDeng YMao JMirrokni VZuo S(2023)Optimal Mechanisms for a Value Maximizer: The Futility of Screening TargetsSSRN Electronic Journal10.2139/ssrn.4351927Online publication date: 2023
https://doi.org/10.2139/ssrn.4351927
Assadi SKher VLi GSchvartzman ALeyton-Brown KSamuelson LHartline J(2023)Fine-Grained Buy-Many Mechanisms Are Not Much Better Than BundlingProceedings of the 24th ACM Conference on Economics and Computation10.1145/3580507.3597662(123-152)Online publication date: 9-Jul-2023
https://dl.acm.org/doi/10.1145/3580507.3597662
Weinberg SZhou ZPennock DSegal ISeuken S(2022)Optimal Multi-Dimensional Mechanisms are not Locally-ImplementableProceedings of the 23rd ACM Conference on Economics and Computation10.1145/3490486.3538334(875-896)Online publication date: 12-Jul-2022
https://dl.acm.org/doi/10.1145/3490486.3538334
Chawla STeng YTzamos C(2022)Buy-many mechanisms are not much better than item pricingGames and Economic Behavior10.1016/j.geb.2022.04.003134(104-116)Online publication date: Jul-2022
https://doi.org/10.1016/j.geb.2022.04.003
Babaioff MGonczarowski YNisan N(2022)The menu-size complexity of revenue approximationGames and Economic Behavior10.1016/j.geb.2021.03.001134(281-307)Online publication date: Jul-2022
https://doi.org/10.1016/j.geb.2021.03.001
Rubinstein AZhao J(2021)The randomized communication complexity of revenue maximizationACM SIGecom Exchanges10.1145/3505156.350516519:2(75-83)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.1145/3505156.3505165
Gonczarowski YWeinberg S(2021)The Sample Complexity of Up-to-ε Multi-dimensional Revenue MaximizationJournal of the ACM10.1145/343972268:3(1-28)Online publication date: 22-Mar-2021
https://dl.acm.org/doi/10.1145/3439722
Cheng YGravin NMunagala KWang K(2021)A Simple Mechanism for a Budget-Constrained BuyerACM Transactions on Economics and Computation10.1145/34344199:2(1-25)Online publication date: 4-Jan-2021
https://dl.acm.org/doi/10.1145/3434419
Rubinstein AZhao JKhuller SVassilevska Williams V(2021)The randomized communication complexity of randomized auctionsProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451111(882-895)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451111
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Cited By

Index Terms

Recommendations

Bounding the menu-size of approximately optimal auctions via optimal-transport duality

Mixed-bundling auctions with reserve prices

On Envy-Free Revenue Approximation for Combinatorial Buyers with Budgets