On Symmetries in Multi-dimensional Mechanism Design

Meryem Essaidi, S. Matthew Weinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


We consider a revenue-maximizing seller with multiple items for sale to a single population of buyers. Our main result shows that for a single population of additive buyers with independent (but not necessarily identically distributed) item values, bundling all items together achieves a constant-factor approximation to the revenue-optimal item-symmetric mechanism. We further motivate this direction via fairness in ad auctions. In ad auction domains the items correspond to views from particular demographics, and recent works have therefore identified a novel fairness constraint: equally-qualified users from different demographics should be shown the same desired ad at equal rates. Prior work abstracts this to the following fairness guarantee: if an advertiser places an identical bid on two users, those two users should view the ad with the same probability [27, 34]. We first propose a relaxation of this guarantee from worst-case to Bayesian settings, which circumvents strong impossibility results from these works, and then study this guarantee through the lens of symmetries, as any item-symmetric auction is also fair (by this definition). Observe that in this domain, bundling all items together corresponds to concealing all demographic data [23].

Original languageEnglish (US)
Title of host publicationWeb and Internet Economics - 17th International Conference, WINE 2021, Proceedings
EditorsMichal Feldman, Hu Fu, Inbal Talgam-Cohen
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783030946753
StatePublished - 2022
Event17th International Conference on Web and Internet Economics, WINE 2021 - Virtual, Online
Duration: Dec 14 2021Dec 17 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13112 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Conference on Web and Internet Economics, WINE 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


  • Fairness
  • Multi-dimensional ad auctions
  • Symmetry


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