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.
|Title of host publication
|STOC 2015 - Proceedings of the 2015 ACM Symposium on Theory of Computing
|Association for Computing Machinery
|Number of pages
|Published - 14 Jun 2015
|47th Annual ACM Symposium on Theory of Computing, STOC 2015 - Portland, United States
Duration: 14 Jun 2015 → 17 Jun 2015
|Proceedings of the Annual ACM Symposium on Theory of Computing
|47th Annual ACM Symposium on Theory of Computing, STOC 2015
|14/06/15 → 17/06/15
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