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Using lotteries in auctions when buyers collude

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Author Info
Nicolas Gruyer () (LEEA (air transport economics laboratory), ENAC)
Abstract

This paper studies the optimal auction for a seller who is bound to sell a single item to one of two potential buyers organized in a ”well-coordinated” cartel. After discussing the way the cartel reacts to any auction mechanism, we show that if the seller has no way to deter collusion, he can still accomodate it optimally with a very simple mechanism, either having the cartel pay to get an efficient allocation or randomly allocating the item. We then discuss the way to implement this mechanism, so that it enables a fair amount of competition if the seller made a mistake and the buyers don’t collude. We find that a simple implementation using reserve prices and lotteries may yield expected revenues close to the optimum if buyers compete, while highly increasing expected revenues if they collude. Finally, we discuss the extension to the n-buyers case.

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Paper provided by LEEA (air transport economics laboratory), ENAC (french national civil aviation school) in its series Economics Working Papers with number 02.

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Length: 30 pages
Date of creation: 04 Oct 2005
Date of revision:
Handle: RePEc:enc:abcdef:auction2

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Related research
Keywords: auctions; optimal auctions; collusion; cartel; mechanism design; auction theory;

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Find related papers by JEL classification:
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions

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  1. Owen R. Phillips & Dale J. Menkhaus & Kalyn T. Coatney, 2003. "Collusive Practices in Repeated English Auctions: Experimental Evidence on Bidding Rings," American Economic Review, American Economic Association, vol. 93(3), pages 965-979, June. [Downloadable!]
  2. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August. [Downloadable!] (restricted)
  3. Aoyagi, Masaki, 2007. "Efficient collusion in repeated auctions with communication," Journal of Economic Theory, Elsevier, vol. 134(1), pages 61-92, May. [Downloadable!] (restricted)
  4. Baldwin, Laura H & Marshall, Robert C & Richard, Jean-Francois, 1997. "Bidder Collusion at Forest Service Timber Sales," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 657-99, August.
  5. Fudenberg, Drew & Levine, David I & Maskin, Eric, 1994. "The Folk Theorem with Imperfect Public Information," Econometrica, Econometric Society, vol. 62(5), pages 997-1039, September. [Downloadable!] (restricted)
    Other versions:
  6. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September. [Downloadable!] (restricted)
    Other versions:
  7. William S. Comanor & Mark A. Schankerman, 1976. "Identical Bids and Cartel Behavior," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 281-286, Spring. [Downloadable!] (restricted)
  8. Hay, George A & Kelley, Daniel, 1974. "An Empirical Survey of Price Fixing Conspiracies," Journal of Law & Economics, University of Chicago Press, vol. 17(1), pages 13-38, April.
  9. Andreas Blume & Paul Heidhues, 2001. "Tacit Collusion in Repeated Auctions," CIG Working Papers FS IV 01-23, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG). [Downloadable!]
  10. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June. [Downloadable!] (restricted)
  11. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-65, Autumn.
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  12. Robert H. Porter & J. Douglas Zona, 1999. "Ohio School Milk Markets: An Analysis of Bidding," RAND Journal of Economics, The RAND Corporation, vol. 30(2), pages 263-288, Summer. [Downloadable!] (restricted)
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  13. Aoyagi, Masaki, 2003. "Bid rotation and collusion in repeated auctions," Journal of Economic Theory, Elsevier, vol. 112(1), pages 79-105, September. [Downloadable!] (restricted)
  14. Pesendorfer, Martin, 2000. "A Study of Collusion in First-Price Auctions," Review of Economic Studies, Blackwell Publishing, vol. 67(3), pages 381-411, July.
  15. Skrzypacz, Andrzej & Hopenhayn, Hugo, 2004. "Tacit collusion in repeated auctions," Journal of Economic Theory, Elsevier, vol. 114(1), pages 153-169, January. [Downloadable!] (restricted)
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  16. Cramton, Peter C & Palfrey, Thomas R, 1990. "Cartel Enforcement with Uncertainty about Costs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 17-47, February. [Downloadable!] (restricted)
    Other versions:
  17. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November. [Downloadable!] (restricted)
    Other versions:
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