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Quadratic Core-Selecting Payment Rules for Combinatorial Auctions

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Abstract

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe. Specifically, we compute a unique point in the core that minimizes the sum of squared deviations from a reference point, for example, from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a series of economically meaningful and equitable penalties. Furthermore, we discuss the benefits of this combinatorial auction, explore the use of alternative reserve pricing approaches in this context, and indicate the results of several hundred computational runs using CATS data.

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File URL: http://www.cramton.umd.edu/papers2005-2009/day-cramton-core-payments-for-combinatorial-auctions.pdf
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Bibliographic Info

Paper provided by University of Maryland, Department of Economics - Peter Cramton in its series Papers of Peter Cramton with number 08qcspr.

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Length: 15 pages
Date of creation: 2008
Date of revision: 2012
Publication status: Published in Operations Research, 60:3, 588-603, 2012
Handle: RePEc:pcc:pccumd:08qcspr

Contact details of provider:
Postal: Economics Department, University of Maryland, College Park, MD 20742-7211
Phone: (202) 318-0520
Fax: (202) 318-0520
Web page: http://www.cramton.umd.edu

Related research

Keywords: Auctions; spectrum auctions; market design; package auction; clock auction; combinatorial auction;

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References

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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. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  3. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
  4. Lawrence M. Ausubel & Peter Cramton & Paul Milgrom, 2004. "The Clock-Proxy Auction: A Practical Combinatorial Auction Design," Papers of Peter Cramton 04mit5, University of Maryland, Department of Economics - Peter Cramton, revised 2004.
  5. Bernheim, B Douglas & Whinston, Michael D, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, MIT Press, vol. 101(1), pages 1-31, February.
  6. Robert W. Day & S. Raghavan, 2007. "Fair Payments for Efficient Allocations in Public Sector Combinatorial Auctions," Management Science, INFORMS, vol. 53(9), pages 1389-1406, September.
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Citations

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Cited by:
  1. Sano, Ryuji, 2012. "Non-bidding equilibrium in an ascending core-selecting auction," Games and Economic Behavior, Elsevier, vol. 74(2), pages 637-650.
  2. Jeremy Bulow & Jonathan Levin & Paul Milgrom, 2009. "Winning Play in Spectrum Auctions," Discussion Papers 08-023, Stanford Institute for Economic Policy Research.
  3. Erdil, Aytek & Klemperer, Paul, 2009. "A New Payment Rule for Core-Selecting Package Auctions," CEPR Discussion Papers 7487, C.E.P.R. Discussion Papers.
  4. Mochon, A. & Saez, Y. & Gomez-Barroso, J.L. & Isasi, P., 2012. "Exploring pricing rules in combinatorial sealed-bid auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 462-478.
  5. Jacob K. Goeree & Yuanchuan Lien, 2009. "On the impossibility of core-selecting auctions," IEW - Working Papers 452, Institute for Empirical Research in Economics - University of Zurich.

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