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An Ascending Vickrey Auction for Selling Bases of a Matroid

Author

Listed:
  • Sushil Bikhchandani

    (Anderson Graduate School of Management, University of California, Los Angeles, Los Angeles, California 90095)

  • Sven de Vries

    (FB IV--Mathematik, Universität Trier, 54286 Trier, Germany)

  • James Schummer

    (Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

  • Rakesh V. Vohra

    (Department of Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208)

Abstract
Consider selling bundles of indivisible goods to buyers with concave utilities that are additively separable in money and goods. We propose an ascending auction for the case when the seller is constrained to sell bundles whose elements form a basis of a matroid. It extends easily to polymatroids. Applications include scheduling, allocation of homogeneous goods, and spatially distributed markets, among others. Our ascending auction induces buyers to bid truthfully and returns the economically efficient basis. Unlike other ascending auctions for this environment, ours runs in pseudopolynomial or polynomial time. Furthermore, we prove the impossibility of an ascending auction for nonmatroidal independence set -systems.

Suggested Citation

  • Sushil Bikhchandani & Sven de Vries & James Schummer & Rakesh V. Vohra, 2011. "An Ascending Vickrey Auction for Selling Bases of a Matroid," Operations Research, INFORMS, vol. 59(2), pages 400-413, April.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:2:p:400-413
    DOI: 10.1287/opre.1100.0888
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    References listed on IDEAS

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    1. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    2. Makowski, Louis & Ostroy, Joseph M., 1987. "Vickrey-Clarke-Groves mechanisms and perfect competition," Journal of Economic Theory, Elsevier, vol. 42(2), pages 244-261, August.
    3. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
    4. Elena Grigorieva & P. Herings & Rudolf Müller & Dries Vermeulen, 2007. "The private value single item bisection auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 107-118, January.
    5. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.
    6. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    7. Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
    8. J. George Shanthikumar & David D. Yao, 1992. "Multiclass Queueing Systems: Polymatroidal Structure and Optimal Scheduling Control," Operations Research, INFORMS, vol. 40(3-supplem), pages 293-299, June.
    9. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    10. Awi Federgruen & Henry Groenevelt, 1986. "Optimal Flows in Networks with Multiple Sources and Sinks, with Applications to Oil and Gas Lease Investment Programs," Operations Research, INFORMS, vol. 34(2), pages 218-225, April.
    11. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    12. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    13. de Vries, Sven & Schummer, James & Vohra, Rakesh V., 2007. "On ascending Vickrey auctions for heterogeneous objects," Journal of Economic Theory, Elsevier, vol. 132(1), pages 95-118, January.
    14. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
    15. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    16. Motty Perry & Philip J. Reny, 2005. "An Efficient Multi-Unit Ascending Auction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 567-592.
    17. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
    18. Groenevelt, H., 1991. "Two algorithms for maximizing a separable concave function over a polymatroid feasible region," European Journal of Operational Research, Elsevier, vol. 54(2), pages 227-236, September.
    19. Satoru Fujishige, 1980. "Lexicographically Optimal Base of a Polymatroid with Respect to a Weight Vector," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 186-196, May.
    20. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-631, July.
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    11. Goel, Gagan & Mirrokni, Vahab & Paes Leme, Renato, 2020. "Clinching auctions with online supply," Games and Economic Behavior, Elsevier, vol. 123(C), pages 342-358.

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