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Combinatorial Auctions Mathematical Formulations And Open Issues

Author

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  • BEZALEL GAVISH

    (Cox School of Business, Southern Methodist University, Dallas, TX 75205, USA)

Abstract

The widespread use of the Internet fostered the establishment of hundreds of sites that support on-line auctions of products and services, some of which also support combinatorial auctions. Finding the optimal combination of winning bids in combinatorial auctions is a difficult task. This paper presents the combinatorial auction problem, classifies combinatorial auctions by the different procedures used during the bidding process, presents some of the applications of combinatorial auctions, and develops mathematical models of combinatorial auctions. The mathematical models are used to identify some of the problem properties and prove that winner determination in combinatorial auctions has the same level of difficulty as solving the allocation problem facing an auctioneer. The paper concludes with the discussion on some of the complexities involved in combinatorial auctions.

Suggested Citation

  • Bezalel Gavish, 2003. "Combinatorial Auctions Mathematical Formulations And Open Issues," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 5-27.
    • Handle: RePEc:wsi:ijitdm:v:02:y:2003:i:01:n:s0219622003000495
    DOI: 10.1142/S0219622003000495
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    References listed on IDEAS

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    1. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
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    Cited by:

    1. Triki, Chefi & Oprea, Simona & Beraldi, Patriza & Crainic, Teodor Gabriel, 2014. "The stochastic bid generation problem in combinatorial transportation auctions," European Journal of Operational Research, Elsevier, vol. 236(3), pages 991-999.

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