Inapproximability of truthful mechanisms via generalizations of the VC dimension

Amit Daniely; Michael Schapira; Gal Shahaf

doi:10.1145/2746539.2746597

Inapproximability of truthful mechanisms via generalizations of the VC dimension

Amit Daniely, Michael Schapira, Gal Shahaf

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

23 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 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 language	English
Title of host publication	STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
Publisher	Association for Computing Machinery
Pages	401-408
Number of pages	8
ISBN (Electronic)	9781450335362
DOIs	https://doi.org/10.1145/2746539.2746597
State	Published - 14 Jun 2015
Event	47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States Duration: 14 Jun 2015 → 17 Jun 2015

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
Volume	14-17-June-2015
ISSN (Print)	0737-8017

Conference

Conference	47th Annual ACM Symposium on Theory of Computing, STOC 2015
Country/Territory	United States
City	Portland
Period	14/06/15 → 17/06/15

Bibliographical note

Publisher Copyright:
© Copyright 2015 ACM.

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10.1145/2746539.2746597

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Daniely, A., Schapira, M., & Shahaf, G. (2015). Inapproximability of truthful mechanisms via generalizations of the VC dimension. In STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing (pp. 401-408). (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. 14-17-June-2015). Association for Computing Machinery. https://doi.org/10.1145/2746539.2746597

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Daniely, A , Schapira, M & Shahaf, G 2015, Inapproximability of truthful mechanisms via generalizations of the VC dimension. in STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, vol. 14-17-June-2015, Association for Computing Machinery, pp. 401-408, 47th Annual ACM Symposium on Theory of Computing, STOC 2015, Portland, United States, 14/06/15. https://doi.org/10.1145/2746539.2746597

Inapproximability of truthful mechanisms via generalizations of the VC dimension. / Daniely, Amit ; Schapira, Michael; Shahaf, Gal.
STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing. Association for Computing Machinery, 2015. p. 401-408 (Proceedings of the Annual ACM Symposium on Theory of Computing; Vol. 14-17-June-2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Inapproximability of truthful mechanisms via generalizations of the VC dimension

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