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Optimization in electronic markets: examples in combinatorial auctions

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  • Stan van Hoesel

    (University of Maastricht)

  • Rudolf Müller

    (University of Maastricht)

Abstract

Combinatorial auctions provide an important tool for mechanism design in multi-agent systems. When implemented they require to solve combinatorial optimization problems such as set packing and partitioning problems. We present in this paper an analysis of the complexity of the problem to assign bids to bidders in combinatorial auctions. We show that the case of identical assets can be solved in polynomial time. The case of non-identical assets is in its general version NP-hard. Extra structure, like a complete ordering of assets, or mild side conditions make the problem solvable. Finally, we present an algorithm to solve small and medium sized instances in a limited time using standard software.

Suggested Citation

  • Stan van Hoesel & Rudolf Müller, 2001. "Optimization in electronic markets: examples in combinatorial auctions," Netnomics, Springer, vol. 3(1), pages 23-33, June.
    • Handle: RePEc:kap:netnom:v:3:y:2001:i:1:d:10.1023_a:1009940607600
    DOI: 10.1023/A:1009940607600
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    References listed on IDEAS

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    1. Ken Binmore & Nir Vulkan, 1999. "Applying game theory to automated negotiation," Netnomics, Springer, vol. 1(1), pages 1-9, October.
    2. Ken Binmore & Nir Vulkan, "undated". "Applying Game Theory to Automated Negotiation," ELSE working papers 004, ESRC Centre on Economics Learning and Social Evolution.
    3. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
    4. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
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    Cited by:

    1. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2009. "Non-linear anonymous pricing combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 296-302, November.
    2. Dries R. Goossens & Sander Onderstal & Jan Pijnacker & Frits C. R. Spieksma, 2014. "Solids: A Combinatorial Auction for Real Estate," Interfaces, INFORMS, vol. 44(4), pages 351-363, August.
    3. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    4. Jing Yu & Lining Xing & Xu Tan, 0. "The new treatment mode research of hepatitis B based on ant colony algorithm," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.
    5. Jing Yu & Lining Xing & Xu Tan, 2021. "The new treatment mode research of hepatitis B based on ant colony algorithm," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 740-759, November.

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