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Reflections about pseudo-dual prices in combinatorial auctions

Author

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  • Drexl, Andreas

    () (Lehrstuhl für Produktion und Logistik, Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität zu Kiel)

  • Jörnsten, Kurt

    () (Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration)

Abstract

Combinatorial auctions permitting bids on bundles of items have been developed to remedy the exposure problem associated with single-item auctions. Given winning bundle prices a set of item prices is called market clearing or equilibrium if all the winning (losing) bids are greater (less) than or equal to the total price of the bundle items. However, the prices for individual items are not readily computed once the winner determination problem is solved. This is due to the duality gap of integer programming caused by the indivisibility of the items. In this paper we reflect on the calculation of approximate or pseudo-dual item prices. In particular, we present a novel scheme based on the aggregation of winning bids. Our analysis is illustrated by means of numerical examples.

Suggested Citation

  • Drexl, Andreas & Jörnsten, Kurt, 2005. "Reflections about pseudo-dual prices in combinatorial auctions," Discussion Papers 2005/1, Norwegian School of Economics, Department of Business and Management Science.
  • Handle: RePEc:hhs:nhhfms:2005_001
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    File URL: http://hdl.handle.net/11250/163584
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    References listed on IDEAS

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    1. Peter R. Wurman & Michael P. Wellman, 1999. "Equilibrium Prices in Bundle Auctions," Working Papers 99-09-064, Santa Fe Institute.
    2. Anthony M. Kwasnica & John O. Ledyard & Dave Porter & Christine DeMartini, 2005. "A New and Improved Design for Multiobject Iterative Auctions," Management Science, INFORMS, vol. 51(3), pages 419-434, March.
    3. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    4. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
    5. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    6. Xia, Mu & Koehler, Gary J. & Whinston, Andrew B., 2004. "Pricing combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 154(1), pages 251-270, April.
    7. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
    8. R. H. Kwon & G. Anandalingam & L. H. Ungar, 2005. "Iterative Combinatorial Auctions with Bidder-Determined Combinations," Management Science, INFORMS, vol. 51(3), pages 407-418, March.
    9. Paul J. Brewer, 1999. "Decentralized computation procurement and computational robustness in a smart market," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(1), pages 41-92.
    10. Delorme, Xavier & Gandibleux, Xavier & Rodriguez, Joaquin, 2004. "GRASP for set packing problems," European Journal of Operational Research, Elsevier, vol. 153(3), pages 564-580, March.
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    Citations

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    Cited by:

    1. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2005. "Non-linear anonymous pricing in combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 598, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    2. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2007. "Column aggregation-based pricing combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 624, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    3. Drexl, Andreas & Jörnsten, Kurt & Knof, Diether, 2005. "Non-linear anonymous pricing in combinatorial auctions," Discussion Papers 2005/6, Norwegian School of Economics, Department of Business and Management Science.
    4. Drexl, Andreas & Jørnsten, Kurt & Knof, Diether, 2007. "Non-linear anonymous pricing combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 625, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    5. M. Iftekhar & A. Hailu & R. Lindner, 2012. "The Effect of Bidder Heterogeneity on Combinatorial Conservation Auction Designs," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 53(1), pages 137-157, September.

    More about this item

    Keywords

    Combinatorial auctions; set packing; dual prices;

    JEL classification:

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

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