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Author Lavi, Ron ♦ Swamy, Chaitanya
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2011
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Combinatorial auction ♦ Truthful and computationally-efficient mechanisms
Abstract We give a general technique to obtain approximation mechanisms that are truthful in expectation. We show that for packing domains, any $\textit{α}-approximation$ algorithm that also bounds the integrality gap of the LP relaxation of the problem by $\textit{α}$ can be used to construct an $\textit{α}-approximation$ mechanism that is truthful in expectation. This immediately yields a variety of new and significantly improved results for various problem domains and furthermore, yields truthful (in expectation) mechanisms with guarantees that match the best-known approximation guarantees when truthfulness is not required. In particular, we obtain the first truthful mechanisms with approximation guarantees for a variety of multiparameter domains. We obtain truthful (in expectation) mechanisms achieving approximation guarantees of $\textit{O}(√\textit{m})$ for combinatorial auctions (CAs), (1 + $\textit{ε})$ for multiunit CAs with $\textit{B}$ = $\textit{Ω}(log$ $\textit{m})$ copies of each item, and 2 for multiparameter knapsack problems (multi-unit auctions). Our construction is based on considering an LP relaxation of the problem and using the classic VCG mechanism to obtain a truthful mechanism in this fractional domain. We argue that the (fractional) optimal solution scaled down by $\textit{α},$ where $\textit{α}$ is the integrality gap of the problem, can be represented as a convex combination of integer solutions, and by viewing this convex combination as specifying a probability distribution over integer solutions, we get a randomized, truthful in expectation mechanism. Our construction can be seen as a way of exploiting VCG in a computational tractable way even when the underlying social-welfare maximization problem is $\textit{NP}-hard.$
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2011-12-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 58
Issue Number 6
Page Count 24
Starting Page 1
Ending Page 24

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Source: ACM Digital Library