Bidding and allocation in combinatorial auctions

Noam Nisan*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

319 Scopus citations


When an auction of multiple items is performed, it is often desirable to allow bids on combinations of items, as opposed to only on single items. Such an auction is often called "combinatorial", and the exponential number of possible combinations results in computational intractability of many aspects regarding such an auction. This paper considers two of these aspects: the bidding language and the allocation algorithm. First we consider which kinds of bids on combinations are allowed and how, i.e. in what language, they are specified. The basic tradeoff is the expressibility of the language versus its simplicity. We consider and formalize several bidding languages and compare their strengths. We prove exponential separations between the expressive power of different languages, and show that one language, "OR-bids with phantom items", can polynomially simulate the others. We then consider the problem of determining the best allocation { a problem known to be computationally intractable. We suggest an approach based on Linear Programming (LP) and motivate it. We prove that the LP approach finds an optimal allocation if and only if prices can be attached to single items in the auction. We pinpoint several classes of auctions where this is the case, and suggest greedy and branch-andbound heuristics based on LP for other cases.

Original languageAmerican English
Title of host publicationEC 2000 - Proceedings of the 2nd ACM Conference on Electronic Commerce
PublisherAssociation for Computing Machinery, Inc
Number of pages12
ISBN (Electronic)9781581132724
StatePublished - 17 Oct 2000
Event2nd ACM Conference on Electronic Commerce, EC 2000 - Minneapolis, United States
Duration: 17 Oct 200020 Oct 2000

Publication series

NameEC 2000 - Proceedings of the 2nd ACM Conference on Electronic Commerce


Conference2nd ACM Conference on Electronic Commerce, EC 2000
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
© 2000 ACM. All rights reserved.


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