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Non-linear anonymous pricing combinatorial auctions

Author

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  • Drexl, Andreas
  • Jørnsten, Kurt
  • Knof, Diether
Abstract
In combinatorial auctions the pricing problem is of main concern since it is the means by which the auctioneer signals the result of the auction to the participants. In order for the auction to be regarded as fair among the various participants the price signals should be such that a participant that has won a subset of items knows why his bid was a winning bid and that agents that have not acquired any item easily can detect why they lost. The problem in the combinatorial auction setting is that the winner determination problem is a hard integer programming problem and hence a linear pricing scheme supporting the optimal allocation might not exist. From integer programming duality theory we know that there exist non-linear anonymous price functions that support the optimal allocation. In this paper we will provide a means to obtain a simple form of a price system that supports the optimal allocation. Our method relies on the fact that we separate the solution of the winner determination problem and the pricing problem. This separation yields a non-linear price function of a much simpler form compared to when the two problems are solved simultaneously. The pure pricing problem is formulated as a mixed-integer program. The procedure is computationally tested using difficult instances of the combinatorial auctions test suite [16]. The results indicate that the number of extreme prices forming the non-linear anonymous price system is small.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:296-302
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    Cited by:

    1. Dirk Briskorn & Kurt Jørnsten & Jenny Nossack, 2016. "Pricing combinatorial auctions by a set of linear price vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 1043-1070, October.
    2. Lam, Jasmine Siu Lee & Gu, Yimiao, 2016. "A market-oriented approach for intermodal network optimisation meeting cost, time and environmental requirements," International Journal of Production Economics, Elsevier, vol. 171(P2), pages 266-274.
    3. Martin Bichler & Pasha Shabalin & Alexander Pikovsky, 2009. "A Computational Analysis of Linear Price Iterative Combinatorial Auction Formats," Information Systems Research, INFORMS, vol. 20(1), pages 33-59, March.
    4. Kemal Guler & Martin Bichler & Ioannis Petrakis, 2016. "Ascending Combinatorial Auctions with Risk Averse Bidders," Group Decision and Negotiation, Springer, vol. 25(3), pages 609-639, May.
    5. Wang, Chao & Guo, Peijun, 2017. "Behavioral models for first-price sealed-bid auctions with the one-shot decision theory," European Journal of Operational Research, Elsevier, vol. 261(3), pages 994-1000.

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    More about this item

    Keywords

    Combinatorial auctions Set packing Strong duality theory Non-linear anonymous pricing;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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