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Using lotteries in auctions when buyers collude

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  • Nicolas Gruyer

    ()
    (LEEA (air transport economics laboratory), ENAC)

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    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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    File URL: http://gruyern.free.fr/wpaper/ColAuct.pdf
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    Bibliographic Info

    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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    1. Marshall, R.C. & Richard J.F., 1995. "Bider Collusion at Forest Service Timber Sales," Papers 7-95-3, Pennsylvania State - Department of Economics.
    2. Aoyagi, Masaki, 2003. "Bid rotation and collusion in repeated auctions," Journal of Economic Theory, Elsevier, vol. 112(1), pages 79-105, September.
    3. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    5. J. Riley & E. Maskin, 1981. "Optimal Auctions with Risk Averse Buyers," Working papers 311, Massachusetts Institute of Technology (MIT), Department of Economics.
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    7. 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.
    8. Pesendorfer, Martin, 2000. "A Study of Collusion in First-Price Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 381-411, July.
    9. 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.
    10. Hay, George A & Kelley, Daniel, 1974. "An Empirical Survey of Price Fixing Conspiracies," Journal of Law and Economics, University of Chicago Press, vol. 17(1), pages 13-38, April.
    11. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    12. Peter Cramton & Thomas R. Palfrey, 1991. "Cartel Enforcement with Uncertainty About Costs," Papers of Peter Cramton 90ier, University of Maryland, Department of Economics - Peter Cramton, revised 09 Jun 1998.
    13. 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.
    14. 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).
    15. Graham, Daniel A & Marshall, Robert C, 1987. "Collusive Bidder Behavior at Single-Object Second-Price and English Auctions," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1217-39, December.
    16. Aoyagi, Masaki, 2007. "Efficient collusion in repeated auctions with communication," Journal of Economic Theory, Elsevier, vol. 134(1), pages 61-92, May.
    17. 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.
    18. McAfee, R. Preston & McMillan, John., 1990. "Bidding Rings," Working Papers 726, California Institute of Technology, Division of the Humanities and Social Sciences.
    19. 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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