Inapproximability of Truthful Mechanisms via Generalizations of the VC Dimension release_4odn46dwofdmflwhc6sjrtvcli

by Amit Daniely and Michael Schapira and Gal Shahaf

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2015  

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.
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Date   2015-04-04
Version   v2
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arXiv  1412.6265v2
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