Inapproximability of Truthful Mechanisms via Generalizations of the VC
Dimension
release_4odn46dwofdmflwhc6sjrtvcli
by
Amit Daniely and Michael Schapira and Gal Shahaf
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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