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Iterative Combinatorial Auctions with Bidder-Determined Combinations

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  • R. H. Kwon

    () (Department of Mechanical and Industrial Engineering, University of Toronto, Ontario, Canada, M5S 3G8)

  • G. Anandalingam

    () (The Robert H. Smith School of Business, University of Maryland, College Park, Maryland 20742)

  • L. H. Ungar

    () (Department of Computer and Information Science, University of Pennsylvania, Pennsylvania 19104)

Abstract

In combinatorial auctions, multiple distinct items are sold simultaneously and a bidder may place a single bid on a set (package) of distinct items. The determination of packages for bidding is a nontrivial task, and existing efficient formats require that bidders know the set of packages and/or their valuations. In this paper, we extend an efficient ascending combinatorial auction mechanism to use approximate single-item pricing. The single-item prices in each round are derived from a linear program that is constructed to reflect the current allocation of packages. Introduction of approximate single-item prices allows for endogenous bid determination where bidders can discover packages that were not included in the original bid set. Due to nonconvexities, single-item prices may not exist that are exact marginal values. We show that the use of approximate single-item prices with endogenous bidding always produces allocations that are at least as efficient as those from bidding with a fixed set of packages based on package pricing. A network resource allocation example is given that illustrates the benefits of our endogenous bidding mechanism.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:3:p:407-418
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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0335
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    References listed on IDEAS

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    12. Hobbs, Benjamin F. & Rothkopf, Michael H. & Hyde, Laurel C. & O'Neill, Richard P., 2000. "Evaluation of a Truthful Revelation Auction in the Context of Energy Markets with Nonconcave Benefits," Journal of Regulatory Economics, Springer, vol. 18(1), pages 5-32, July.
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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, 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.
    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. repec:pal:jorsoc:v:58:y:2007:i:12:d:10.1057_palgrave.jors.2602299 is not listed on IDEAS
    5. repec:eee:transe:v:107:y:2017:i:c:p:60-80 is not listed on IDEAS
    6. Axel Ockenfels & David Reiley & Abdolkarim Sadrieh, 2006. "Online Auctions," NBER Working Papers 12785, National Bureau of Economic Research, Inc.
    7. G. Anandalingam & Robert W. Day & S. Raghavan, 2005. "The Landscape of Electronic Market Design," Management Science, INFORMS, vol. 51(3), pages 316-327, March.
    8. 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.
    9. Schneider, S. & Shabalin, P. & Bichler, M., 2010. "On the robustness of non-linear personalized price combinatorial auctions," European Journal of Operational Research, Elsevier, vol. 206(1), pages 248-259, October.
    10. Drexl, Andreas & Jörnsten, Kurt, 2005. "Reflections about pseudo-dual prices in combinatorial auctions," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 590, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    11. 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.
    12. 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.
    13. Triki, Chefi & Oprea, Simona & Beraldi, Patriza & Crainic, Teodor Gabriel, 2014. "The stochastic bid generation problem in combinatorial transportation auctions," European Journal of Operational Research, Elsevier, vol. 236(3), pages 991-999.
    14. repec:eee:transe:v:106:y:2017:i:c:p:137-159 is not listed on IDEAS
    15. Avenali, Alessandro, 2009. "Exploring the VCG mechanism in combinatorial auctions: The threshold revenue and the threshold-price rule," European Journal of Operational Research, Elsevier, vol. 199(1), pages 262-275, November.
    16. Ervasti, Valtteri & Leskelä, Riikka-Leena, 2010. "Allocative efficiency in simulated multiple-unit combinatorial auctions with quantity support," European Journal of Operational Research, Elsevier, vol. 203(1), pages 251-260, May.

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