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An Ascending Vickrey Auction for Selling Bases of a Matroid

Author

Listed:
  • Sushil Bikhchandani
  • Sven de Vries
  • James Schummer
  • Rakesh V. Vohra

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.
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Suggested Citation

  • Sushil Bikhchandani & Sven de Vries & James Schummer & Rakesh V. Vohra, 2005. "An Ascending Vickrey Auction for Selling Bases of a Matroid," Levine's Bibliography 784828000000000133, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:784828000000000133
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    File URL: http://www.anderson.ucla.edu/faculty/sushil.bikhchandani/papers/jvickMay2005.pdf
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    Cited by:

    1. Moulin, Hervé & Velez, Rodrigo A., 2013. "The price of imperfect competition for a spanning network," Games and Economic Behavior, Elsevier, vol. 81(C), pages 11-26.
    2. Ozan Candogan & Saša Pekeč, 2018. "Efficient Allocation and Pricing of Multifeatured Items," Management Science, INFORMS, vol. 64(12), pages 5521-5543, December.
    3. Kevin Leyton-Brown & Paul Milgrom & Neil Newman & Ilya Segal, 2024. "Artificial Intelligence and Market Design: Lessons Learned from Radio Spectrum Reallocation," NBER Chapters, in: New Directions in Market Design, National Bureau of Economic Research, Inc.
    4. Neil Newman & Kevin Leyton-Brown & Paul Milgrom & Ilya Segal, 2024. "Incentive Auction Design Alternatives: A Simulation Study," Management Science, INFORMS, vol. 70(11), pages 8187-8215, November.
    5. Aadityan Ganesh & Jason Hartline, 2023. "Combinatorial Pen Testing (or Consumer Surplus of Deferred-Acceptance Auctions)," Papers 2301.12462, arXiv.org, revised Dec 2024.
    6. Paul Dütting & Vasilis Gkatzelis & Tim Roughgarden, 2017. "The Performance of Deferred-Acceptance Auctions," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 897-914, November.
    7. Li, Yunan, 2017. "Approximation in mechanism design with interdependent values," Games and Economic Behavior, Elsevier, vol. 103(C), pages 225-253.
    8. Ozan Candogan & Asuman Ozdaglar & Pablo A. Parrilo, 2015. "Iterative Auction Design for Tree Valuations," Operations Research, INFORMS, vol. 63(4), pages 751-771, August.
    9. Chen, Ning & Ghosh, Arpita & Lambert, Nicolas S., 2014. "Auctions for social lending: A theoretical analysis," Games and Economic Behavior, Elsevier, vol. 86(C), pages 367-391.
    10. Andersson, Tommy & Erlanson, Albin, 2013. "Multi-item Vickrey–English–Dutch auctions," Games and Economic Behavior, Elsevier, vol. 81(C), pages 116-129.
    11. Eickhoff, Katharina & Neuwohner, Meike & Peis, Britta & Rieken, Niklas & Vargas Koch, Laura & Végh, Lázló A., 2025. "Faster dynamic auctions via polymatroid sum," LSE Research Online Documents on Economics 127980, London School of Economics and Political Science, LSE Library.
    12. Jorge Barrera & Alfredo Garcia, 2015. "Auction Design for the Efficient Allocation of Service Capacity Under Congestion," Operations Research, INFORMS, vol. 63(1), pages 151-165, February.
    13. 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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