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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.

Suggested Citation

  • Robert Day & Peter Cramton, 2008. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Papers of Peter Cramton 08qcspr, University of Maryland, Department of Economics - Peter Cramton, revised 2012.
  • Handle: RePEc:pcc:pccumd:08qcspr
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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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    References listed on IDEAS

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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. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    3. 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.
    4. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    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. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 393-407, March.
    7. 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.
    8. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
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    Citations

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    Cited by:

    1. Christian Kroemer & Martin Bichler & Andor Goetzendorff, 2016. "(Un)expected Bidder Behavior in Spectrum Auctions: About Inconsistent Bidding and Its Impact on Efficiency in the Combinatorial Clock Auction," Group Decision and Negotiation, Springer, vol. 25(1), pages 31-63, January.
    2. Goeree, Jacob K. & Lien, Yuanchuan, 2016. "On the impossibility of core-selecting auctions," Theoretical Economics, Econometric Society, vol. 11(1), January.
    3. repec:oup:oxford:v:33:y:2017:i:4:p:541-571. is not listed on IDEAS
    4. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press, vol. 33(4), pages 541-571.
    5. Jeremy Bulow & Jonathan Levin & Paul Milgrom, 2009. "Winning Play in Spectrum Auctions," Discussion Papers 08-023, Stanford Institute for Economic Policy Research.
    6. Isa Hafalir & Hadi Yektaş, 2015. "Core deviation minimizing auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 367-376, May.
    7. Ryuji Sano, 2015. "Improving Efficiency Using Reserve Prices: An Equilibrium Analysis of Core-Selecting Auctions," KIER Working Papers 926, Kyoto University, Institute of Economic Research.
    8. Sano, Ryuji, 2012. "Non-bidding equilibrium in an ascending core-selecting auction," Games and Economic Behavior, Elsevier, vol. 74(2), pages 637-650.
    9. Todd R. Kaplan & Shmuel Zamir, 2014. "Advances in Auctions," Discussion Papers 1405, Exeter University, Department of Economics.
    10. Kemal Guler & Martin Bichler & Ioannis Petrakis, 2016. "Ascending Combinatorial Auctions with Risk Averse Bidders," Group Decision and Negotiation, Springer, vol. 25(3), pages 609-639, May.
    11. Daniel Marszalec, 2016. "Auctions For Complements –An Experimental Analysis," CIRJE F-Series CIRJE-F-1018, CIRJE, Faculty of Economics, University of Tokyo.
    12. Bichler, Martin & Goeree, Jacob K., 2017. "Frontiers in spectrum auction design," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 372-391.
    13. Peter Cramton, 2013. "Spectrum Auction Design," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 42(2), pages 161-190, March.
    14. Aytek Erdil & Paul Klemperer, 2010. "A New Payment Rule for Core-Selecting Package Auctions," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 537-547, 04-05.
    15. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications, Elsevier.
    16. Lawrence M. Ausubel & Oleg V. Baranov, 2014. "Market Design and the Evolution of the Combinatorial Clock Auction," American Economic Review, American Economic Association, vol. 104(5), pages 446-451, May.
    17. 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.

    More about this item

    Keywords

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

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • L96 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Telecommunications

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