Inapproximability of truthful mechanisms via generalizations of the Vapnik--Chervonenkis dimension

Amit Daniely, Michael Schapira, And G.A.L. Shahaf

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 Vapnik–Chervonenkis (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 nontruthful algorithms.

Original languageAmerican English
Pages (from-to)96-120
Number of pages25
JournalSIAM Journal on Computing
Volume47
Issue number1
DOIs
StatePublished - 2018

Bibliographical note

Funding Information:
The first author was supported, in part, by the Google Europe Fellowship in Learning Theory.

Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.

Keywords

  • AGT
  • Auctions
  • VC dimension

Fingerprint

Dive into the research topics of 'Inapproximability of truthful mechanisms via generalizations of the Vapnik--Chervonenkis dimension'. Together they form a unique fingerprint.

Cite this