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Iterative Combinatorial Auctions with Bidder-Determined Combinations

  • 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)

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    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.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 51 (2005)
    Issue (Month): 3 (March)
    Pages: 407-418

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    Handle: RePEc:inm:ormnsc:v:51:y:2005:i:3:p:407-418
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    1. 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.
    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. Hobbs, Benjamin F, et al, 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.
    4. Frank Kelly & Richard Steinberg, 2000. "A Combinatorial Auction with Multiple Winners for Universal Service," Management Science, INFORMS, vol. 46(4), pages 586-596, April.
    5. Milgrom, Paul, 1998. "Putting auction theory to work : the simultaneous ascending auction," Policy Research Working Paper Series 1986, The World Bank.
    6. Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February.
    7. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    8. Peter Cramton & John McMillan & Paul Milgrom & Bradley Miller & Bridger Mitchell & Daniel Vincent & Robert Wilson, 1998. "Simultaneous Ascending Auctions with Package Bidding," Papers of Peter Cramton 98cra2, University of Maryland, Department of Economics - Peter Cramton.
    9. 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.
    10. 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.
    11. Rothkopf, Michael H & Harstad, Ronald M, 1995. "Two Models of Bid-Taker Cheating in Vickrey Auctions," The Journal of Business, University of Chicago Press, vol. 68(2), pages 257-67, April.
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