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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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  • 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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    1. 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.
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    6. Laurent Lamy, 2010. "Core-selecting package auctions: a comment on revenue-monotonicity," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 503-510, July.
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    13. 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.
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    More about this item

    Keywords

    Auctions; spectrum auctions; market design; package auction; clock auction; combinatorial auction;
    All these keywords.

    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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