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Auctions with Almost Homogeneous Bidders

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  • Bernard Lebrun

    () (Department of Economics, York University)

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.

Suggested Citation

  • Bernard Lebrun, 2006. "Auctions with Almost Homogeneous Bidders," Working Papers 2006_7, York University, Department of Economics.
  • Handle: RePEc:yca:wpaper:2006_7
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    File URL: http://dept.econ.yorku.ca/research/workingPapers/working_papers/2006/auctalmhombid-wp-lebrun.pdf
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    References listed on IDEAS

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    1. Thomas, Charles J., 1997. "Disincentives for cost-reducing investment," Economics Letters, Elsevier, vol. 57(3), pages 359-363, December.
    2. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
    3. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    4. Lebrun, Bernard, 1998. "Comparative Statics in First Price Auctions," Games and Economic Behavior, Elsevier, vol. 25(1), pages 97-110, October.
    5. Leandro Arozamena & Estelle Cantillon, 2004. "Investment Incentives in Procurement Auctions," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 1-18.
    6. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    7. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    8. Waehrer, Keith, 1999. "Asymmetric private values auctions with application to joint bidding and mergers," International Journal of Industrial Organization, Elsevier, vol. 17(3), pages 437-452, April.
    9. 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 125-142, February.
    10. Fibich, Gadi & Gavious, Arieh & Sela, Aner, 2004. "Revenue equivalence in asymmetric auctions," Journal of Economic Theory, Elsevier, vol. 115(2), pages 309-321, April.
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    Cited by:

    1. Fibich, Gadi & Gavish, Nir, 2011. "Numerical simulations of asymmetric first-price auctions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 479-495.
    2. Kirkegaard, René, 2013. "Incomplete information and rent dissipation in deterministic contests," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 261-266.
    3. Arieh Gavious & Yizhaq Minchuk, 2014. "Ranking asymmetric auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 369-393, May.
    4. Fibich, Gadi & Gavious, Arieh, 2010. "Asymptotic revenue equivalence of asymmetric auctions with interdependent values," European Journal of Operational Research, Elsevier, vol. 206(2), pages 496-507, October.

    More about this item

    Keywords

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

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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