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Pre-Auction Offers in Asymmetric First-Price and Second-Price Auctions

  • René Kirkegaard

    (Brock University)

  • Per Baltzer Overgaard

    (School of Economics and Management, University of Aarhus)

We consider “must-sell” auctions with asymmetric buyers. First, we study auctions with two asymmetric buyers, where the distribution of valuations of the strong buyer is “stretched” relative to that of the weak buyer. Then, it is known that inefficient first-price auctions are more profitable for the seller than efficient second-price auctions. This is because the former favor the weak buyer. However, we show that the seller can do one better by augmenting the first-price auction by a pre-auction offer made exclusively to the strong buyer. Should the strong buyer reject the offer, the object is simply sold in an ordinary first-price auction. The result is driven by the fact that the unmodified first-price auction is too favorable to the weak buyer, and that the pre-auction offer allows some correction of this to the benefit of the seller. Secondly, we show quite generally that pre-auction offers never increase the profitability of second-price auctions, since they introduce the wrong kind of favoritism from the perspective of seller profits.

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Paper provided by University of Copenhagen. Department of Economics. Centre for Industrial Economics in its series CIE Discussion Papers with number 2005-04.

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Length: 13 pages
Date of creation: Oct 2005
Date of revision:
Handle: RePEc:kud:kuieci:2005-04
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  1. Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-94, March.
  2. Budish, Eric B. & Takeyama, Lisa N., 2001. "Buy prices in online auctions: irrationality on the internet?," Economics Letters, Elsevier, vol. 72(3), pages 325-333, September.
  3. Ivanova-Stenzel, Radosveta & Kröger, Sabine, 2008. "Price formation in a sequential selling mechanism," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 832-843, September.
  4. René Kirkegaard, 2006. "A short proof of the Bulow-Klemperer auctions vs. negotiations result," Economic Theory, Springer, vol. 28(2), pages 449-452, 06.
  5. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-42, February.
  6. Plum, M, 1992. "Characterization and Computation of Nash-Equilibria for Auctions with Incomplete Information," International Journal of Game Theory, Springer, vol. 20(4), pages 393-418.
  7. Giuseppe Lopomo, 2004. "The English Auction Is Optimal Among Simple Sequential Auctions," Levine's Bibliography 122247000000000369, UCLA Department of Economics.
  8. Bulow, Jeremy & Roberts, John, 1989. "The Simple Economics of Optimal Auctions," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1060-90, October.
  9. Hidvegi, Zoltan & Wang, Wenli & Whinston, Andrew B., 2006. "Buy-price English auction," Journal of Economic Theory, Elsevier, vol. 129(1), pages 31-56, July.
  10. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
  11. René Kirkegaard & Per Baltzer Overgaard, 2008. "Buy-out prices in auctions: seller competition and multi-unit demands," RAND Journal of Economics, RAND Corporation, vol. 39(3), pages 770-789.
  12. Blume, Andreas & Heidhues, Paul, 2004. "All equilibria of the Vickrey auction," Journal of Economic Theory, Elsevier, vol. 114(1), pages 170-177, January.
  13. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
  14. Timothy Mathews, 2004. "The Impact of Discounting on an Auction with a Buyout Option: a Theoretical Analysis Motivated by eBay’s Buy-It-Now Feature," Journal of Economics, Springer, vol. 81(1), pages 25-52, 01.
  15. Timothy Mathews, 2003. "A Risk Averse Seller in a Continuous Time Auction with a Buyout Option," Brazilian Electronic Journal of Economics, Department of Economics, Universidade Federal de Pernambuco, vol. 5(2), January.
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