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Reflections about pseudo-dual prices in combinatorial auctions

Author

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  • A Drexl

    (Christian-Albrechts-Universität)

  • K Jørnsten

    (Institute for Research in 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

  • A Drexl & K Jørnsten, 2007. "Reflections about pseudo-dual prices in combinatorial auctions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1652-1659, December.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:12:d:10.1057_palgrave.jors.2602299
    DOI: 10.1057/palgrave.jors.2602299
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    1. 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.
    2. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
    3. Peter R. Wurman & Michael P. Wellman, 1999. "Equilibrium Prices in Bundle Auctions," Working Papers 99-09-064, Santa Fe Institute.
    4. WOLSEY, Laurence A., 1981. "Integer programming duality: price functions and sensitivity analysis," LIDAM Reprints CORE 431, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Herbert E. Scarf, 1990. "Mathematical Programming and Economic Theory," Operations Research, INFORMS, vol. 38(3), pages 377-385, June.
    6. 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.
    7. 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.
    8. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
    9. 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.
    10. Tuomas Sandholm & Subhash Suri & Andrew Gilpin & David Levine, 2005. "CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions," Management Science, INFORMS, vol. 51(3), pages 374-390, March.
    11. 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.
    12. 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.
    13. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    14. Oktay Günlük & Lászlo Ladányi & Sven de Vries, 2005. "A Branch-and-Price Algorithm and New Test Problems for Spectrum Auctions," Management Science, INFORMS, vol. 51(3), pages 391-406, March.
    15. 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.
    16. Karla L. Hoffman & Manfred Padberg, 1993. "Solving Airline Crew Scheduling Problems by Branch-and-Cut," Management Science, INFORMS, vol. 39(6), pages 657-682, June.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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    More about this item

    Keywords

    combinatorial auctions; set packing; dual prices;
    All these keywords.

    JEL classification:

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

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