Truthful approximation mechanisms for restricted combinatorial auctions

Ahuva Mu'alem*, Noam Nisan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

127 Scopus citations

Abstract

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios.

Original languageAmerican English
Pages (from-to)612-631
Number of pages20
JournalGames and Economic Behavior
Volume64
Issue number2
DOIs
StatePublished - Nov 2008

Keywords

  • Approximation algorithms
  • Combinatorial auctions
  • Mechanism design
  • Multi-unit auctions
  • Multi-unit combinatorial auctions

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