Limitations of VCG-based mechanisms

Shahar Dobzinski; Noam Nisan

doi:10.1007/s00493-011-2528-4

Limitations of VCG-based mechanisms

Shahar Dobzinski, Noam Nisan

The Rachel and Selim Benin School of Engineering and Computer Science

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We consider computationally-efficient truthful mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Our technique is based on setting lower bounds on the communication complexity by analyzing combinatorial properties of the algorithms. Specifically, for combinatorial auctions among submodular (and thus also subadditive) bidders we prove an ω(m^1/6)lower bound, which is close to the known upper bound of O(m^1/2), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.

Original language	English
Pages (from-to)	379-396
Number of pages	18
Journal	Combinatorica
Volume	31
Issue number	4
DOIs	https://doi.org/10.1007/s00493-011-2528-4
State	Published - Nov 2011

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/s00493-011-2528-4

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title = "Limitations of VCG-based mechanisms",

abstract = "We consider computationally-efficient truthful mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Our technique is based on setting lower bounds on the communication complexity by analyzing combinatorial properties of the algorithms. Specifically, for combinatorial auctions among submodular (and thus also subadditive) bidders we prove an ω(m1/6)lower bound, which is close to the known upper bound of O(m1/2), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.",

author = "Shahar Dobzinski and Noam Nisan",

note = "Funding Information: Acknowledgements. We thank Liad Blumrosen and Nikhil Devanur for pointing out that the algorithms of [3] and [2] are maximal in range. We also thank Liad Blumrosen for comments on an earlier draft of this paper. This research was supported by a grant from the Israeli Academy of Sciences. The first author is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.",

year = "2011",

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doi = "10.1007/s00493-011-2528-4",

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AU - Nisan, Noam

N1 - Funding Information: Acknowledgements. We thank Liad Blumrosen and Nikhil Devanur for pointing out that the algorithms of [3] and [2] are maximal in range. We also thank Liad Blumrosen for comments on an earlier draft of this paper. This research was supported by a grant from the Israeli Academy of Sciences. The first author is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities.

PY - 2011/11

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N2 - We consider computationally-efficient truthful mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Our technique is based on setting lower bounds on the communication complexity by analyzing combinatorial properties of the algorithms. Specifically, for combinatorial auctions among submodular (and thus also subadditive) bidders we prove an ω(m1/6)lower bound, which is close to the known upper bound of O(m1/2), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.

AB - We consider computationally-efficient truthful mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Our technique is based on setting lower bounds on the communication complexity by analyzing combinatorial properties of the algorithms. Specifically, for combinatorial auctions among submodular (and thus also subadditive) bidders we prove an ω(m1/6)lower bound, which is close to the known upper bound of O(m1/2), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.

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DO - 10.1007/s00493-011-2528-4

M3 - مقالة

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VL - 31

SP - 379

EP - 396

JO - Combinatorica

JF - Combinatorica

IS - 4

ER -

Limitations of VCG-based mechanisms

Abstract

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