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Quadratic Core-Selecting Payment Rules for Combinatorial Auctions

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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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
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  1. B. Douglas Bernheim & Michael D. Whinston, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, Oxford University Press, vol. 101(1), pages 1-31.
  2. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
  3. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  4. Lawrence M. Ausubel & Peter Crampton & Paul Milgrom, 2004. "The Clock-Proxy Auction: A Practical Combinatorial Auction Design," Discussion Papers 03-034, Stanford Institute for Economic Policy Research.
  5. 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.
  6. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
  7. 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.
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