Combinatorial auctions with decreasing marginal utilities

Benny Lehmann, Daniel Lehmann*, Noam Nisan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

299 Scopus citations

Abstract

In most of microeconomic theory, consumers are assumed to exhibit decreasing marginal utilities. This paper considers combinatorial auctions among such submodular buyers. The valuations of such buyers are placed within a hierarchy of valuations that exhibit no complementarities, a hierarchy that includes also OR and XOR combinations of singleton valuations, and valuations satisfying the gross substitutes property. Those last valuations are shown to form a zero-measure subset of the submodular valuations that have positive measure. While we show that the allocation problem among submodular valuations is NP-hard, we present an efficient greedy 2-approximation algorithm for this case and generalize it to the case of limited complementarities. No such approximation algorithm exists in a setting allowing for arbitrary complementarities. Some results about strategic aspects of combinatorial auctions among players with decreasing marginal utilities are also presented.

Original languageAmerican English
Pages (from-to)270-296
Number of pages27
JournalGames and Economic Behavior
Volume55
Issue number2
DOIs
StatePublished - May 2006

Bibliographical note

Funding Information:
✩ A preliminary version of this paper has been presented at EC-2001. Supported by grants from the Israeli Ministry of Science and the Israeli Academy of Sciences. Corresponding author. E-mail addresses: [email protected] (D. Lehmann), [email protected] (N. Nisan). § Benny passed away on July 1st, 2004.

Keywords

  • Combinatorial auctions
  • Decreasing marginal utilities
  • Winner determination

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