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Reflections about pseudo-dual prices in combinatorial auctions

  • 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)

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.

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File URL: http://hdl.handle.net/11250/163584
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Paper provided by Department of Business and Management Science, Norwegian School of Economics in its series Discussion Papers with number 2005/1.

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Length: 15 pages
Date of creation: 26 May 2005
Date of revision:
Handle: RePEc:hhs:nhhfms:2005_001
Contact details of provider: Postal: NHH, Department of Business and Management Science, Helleveien 30, N-5045 Bergen, Norway
Phone: +47 55 95 92 93
Fax: +47 55 95 96 50
Web page: http://www.nhh.no/en/research-faculty/department-of-business-and-management-science.aspx
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  1. Michael H. Rothkopf & Aleksandar Peke\v{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
  2. Milgrom, Paul, 1998. "Putting auction theory to work : the simultaneous ascending auction," Policy Research Working Paper Series 1986, The World Bank.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  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. Paul J. Brewer, 1999. "Decentralized computation procurement and computational robustness in a smart market," Economic Theory, Springer, vol. 13(1), pages 41-92.
  9. Peter R. Wurman & Michael P. Wellman, 1999. "Equilibrium Prices in Bundle Auctions," Working Papers 99-09-064, Santa Fe Institute.
  10. John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
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