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Truthful and Near-Optimal Mechanism Design via Linear Programming

Lavi, Ron and Swamy, Chaitanya (2005) Truthful and Near-Optimal Mechanism Design via Linear Programming. In: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS '05). IEEE , Los Alamitos, CA, pp. 595-604. ISBN 0-7695-2468-0 .

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We give a general technique to obtain approximation mechanisms that are truthful in expectation. We show that for packing domains, any α-approximation algorithm that also bounds the integrality gap of the IF relaxation of the problem by a can be used to construct an 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 multi-parameter domains. We obtain truthful (in expectation) mechanisms achieving approximation guarantees of O(√m) for combinatorial auctions (CAs), (1 + ∈ ) for multiunit CAs with B = Ω(log m) copies of each item, and 2 for multiparameter knapsack problems (multiunit auctions). Our construction is based on considering an LP relaxation of the problem and using the classic VCG mechanism by W. Vickrey (1961), E. Clarke (1971) and T. Groves (1973) to obtain a truthful mechanism in this fractional domain. We argue that the (fractional) optimal solution scaled down by a, where a 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 NP-hard.

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Additional Information:© 2005 IEEE. Issue Date: 23-25 Oct. 2005; Date of Current Version: 14 November 2005. We thank Bruce Shepherd for very useful discussions about the results in [8].
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INSPEC Accession Number8803125
Record Number:CaltechAUTHORS:20110817-152532300
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Official Citation:Lavi, R.; Swamy, C.; , "Truthful and near-optimal mechanism design via linear programming," Foundations of Computer Science, 2005. FOCS 2005. 46th Annual IEEE Symposium on , vol., no., pp. 595- 604, 23-25 Oct. 2005 doi: 10.1109/SFCS.2005.76
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24922
Deposited By: Jason Perez
Deposited On:18 Aug 2011 14:42
Last Modified:23 Aug 2016 10:04

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