Towards a characterization of truthful combinatorial auctions

Ron Lavi*, Ahuva Mu'alem, Noam Nisan

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

158 Scopus citations

Abstract

This paper analyzes incentive compatible (truthful) mechanisms over restricted domains of preferences,. the leading example being combinatorial auctions. Our work generalizes the characterization of Roberts (1979) who showed that truthful mechanisms over unrestricted domains with at least 3 possible outcomes must be "affine maximizers". We show that truthful mechanisms for combinatorial auctions (and related restricted domains) must be "almost affine maximizers" if they also satisfy an additional requirement of "independence of irrelevant alternatives". This requirement is without loss of generality for unrestricted domains as well as for auctions between two players where all goods must be allocated. This implies unconditional results for these cases, including a new proof of Roberts' theorem. The computational implications of this characterization are severe, as reasonable "almost affine maximizers" are shown to be as computationally hard as exact optimization. This implies the near-helplessness of such truthful polynomial-time auctions in all cases where exact optimization is computationally intractable.

Original languageAmerican English
Pages (from-to)574-583
Number of pages10
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 2003
EventProceedings: 44th Annual IEEE Symposium on Foundations of Computer Science - FOCS 2003 - Cambridge, MA, United States
Duration: 11 Oct 200314 Oct 2003

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