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On the impossibility of core-selecting auctions

  • Jacob K. Goeree
  • Yuanchuan Lien

When goods are substitutes, the Vickrey auction produces efficient, core outcomes that yield competitive seller revenues. In contrast, with complements, the Vickrey outcome, while efficient, is not necessarily in the core and revenue can be very low. Non-core outcomes may be perceived as unfair since there are bidders willing to pay more than the winners' payments. Moreover, non-core outcomes render the auction vulnerable to defections as the seller can attract better offers afterwards. To avoid instabilities of this type, Day and Raghavan (2007) and Day and Milgrom (2007) have suggested to adapt the Vickrey pricing rule. For a simple environment with private information, we show that the resulting auction format yields lower than Vickrey revenues and inefficient outcomes that are on average further from the core than Vickrey outcomes. More generally, we prove that the Vickrey auction is the unique core-selecting auction. Hence, when the Vickrey outcome is not in the core, no Bayesian incentive-compatible core-selecting auction exists. Our results further imply that the competitive equilibrium cannot be implemented when goods are not substitutes. Moreover, even with substitutes, the competitive equilibrium can only be implemented when it coincides with the Vickrey outcome.

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Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 452.

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Date of creation: Nov 2009
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Handle: RePEc:zur:iewwpx:452
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  1. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  2. 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.
  3. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
  4. Aytek Erdil & Paul Klemperer, 2009. "A New Payment Rule for Core-Selecting Package Auctions," Economics Papers 2009-W11, Economics Group, Nuffield College, University of Oxford.
  5. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
  6. Roger B. Myerson & Mark A. Satterthwaite, 1981. "Efficient Mechanisms for Bilateral Trading," Discussion Papers 469S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Green, Jerry & Laffont, Jean-Jacques, 1977. "Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods," Econometrica, Econometric Society, vol. 45(2), pages 427-38, March.
  8. 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.
  9. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
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