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Auctions with Almost Homogeneous Bidders

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  • Bernard Lebrun

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    (Department of Economics, York University)

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    Abstract

    We deviate from the symmetric case of the independent private value model by allowing the bidders’ value distributions, which depend on parameters, to be slightly different. We show that previous results about the equality to the first-order in the parameters between revenues from the second-price auction and other auction mechanisms follow from the joint differentiability of the equilibria with respect to the parameters. We prove this differentiability for the first-price auction and obtain general formulas for the different first-order effects. From our results about the first-price auction, we analytically generate examples with continuous distributions where a stochastic improvement to a bidder’s value distribution reduces his equilibrium payoff. In another application, we show that, starting from competition among cartels of equal sizes, allowing in a small number of members from other cartels can be profitable only if the members or the synergies between them are strong enough.

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    File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/2006/auctalmhombid-wp-lebrun.pdf
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    Bibliographic Info

    Paper provided by York University, Department of Economics in its series Working Papers with number 2006_7.

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    Length: 46 pages
    Date of creation: 2006
    Date of revision:
    Handle: RePEc:yca:wpaper:2006_7

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    Related research

    Keywords: Independent private value model; auctions; asymmetry; first-price auction; second-price auction; differentiability; revenue equivalence theorem;

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    References

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    1. Bernard Lebrun, 2004. "Uniqueness of the Equilibrium in First-Price Auctions," Discussion Papers 1, York University, Department of Economics, revised May 2004.
    2. Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2004. "Revenue equivalence in asymmetric auctions," Journal of Economic Theory, Elsevier, vol. 115(2), pages 309-321, April.
    3. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
    4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    5. repec:wop:humbsf:2000-72 is not listed on IDEAS
    6. Thomas, Charles J., 1997. "Disincentives for cost-reducing investment," Economics Letters, Elsevier, vol. 57(3), pages 359-363, December.
    7. Leandro Arozamena & Estelle Cantillon, 2004. "Investment Incentives in Procurement Auctions," Review of Economic Studies, Wiley Blackwell, vol. 71(1), pages 1-18, 01.
    8. 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.
    9. Bernard Lebrun, 2004. "Uniqueness of the Equilibrium in First-Price Auctions," Working Papers 2004_2, York University, Department of Economics.
    10. Maskin, Eric & Riley, John, 2000. "Asymmetric Auctions," Review of Economic Studies, Wiley Blackwell, vol. 67(3), pages 413-38, July.
    11. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
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