Inapproximability of truthful mechanisms via generalizations of the VC dimension

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Abstract

Algorithmic mechanism design (AMD) studies the delicate interplay between computational efficiency, truthfulness, and optimality. We focus on AMD's paradigmatic problem: combinatorial auctions. We present a new generalization of the VC dimension to multivalued collections of functions, which encompasses the classical VC dimension, Natarajan dimension, and Steele dimension. We present a corresponding generalization of the Sauer-Shelah Lemma and harness this VC machinery to establish inapproximability results for deterministic truthful mechanisms. Our results essentially unify all inapproximability results for deterministic truthful mechanisms for combinatorial auctions to date and establish new separation gaps between truthful and non-truthful algorithms.

Original languageAmerican English
Title of host publicationSTOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages401-408
Number of pages8
ISBN (Electronic)9781450335362
DOIs
StatePublished - 14 Jun 2015
Event47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States
Duration: 14 Jun 201517 Jun 2015

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
Volume14-17-June-2015
ISSN (Print)0737-8017

Conference

Conference47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/TerritoryUnited States
CityPortland
Period14/06/1517/06/15

Bibliographical note

Publisher Copyright:
© Copyright 2015 ACM.

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