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Asymmetric Auctions with More Than Two Bidders

Author

Listed:
  • Timothy P. Hubbard

    () (Department of Economics, Colby College)

  • Rene Kirkegaard

    () (Department of Economics and Finance, University of Guelph)

Abstract

The theoretical literature on asymmetric first-price auctions has focused mainly on settings with either (1) exactly two bidders or (2) an arbitrary number of bidders with types in a common support. Even though closed form solutions are typically impossible, there is enough structure in the problem to guide both empirical work and numerical solutions or simulations. However, casual observation of real-world auctions suggests that the assumptions are restrictive. Indeed, the empirical literature has ventured beyond these models. We explain the relevant complications that arise if the above conditions do not hold, emphasizing that the structure of the problem changes significantly. Critically, the dimensionality of the problem appears to increase as bidders may now tender bids over different supports (bid bifurcation). The main conceptual contribution of this paper is to establish a method by which the dimensionality of the problem can once again be reduced. This insight is used to construct the first robust solution algorithm that allows for bid bifurcation. Accurate solution methods are essential to e.g. evaluate different counterfactual policies. We provide sufficient conditions, and in some cases necessary and sufficient conditions, for bid bifurcation to occur and demonstrate its relevance through a series of analytical and numerical examples. Implications for empirical work are emphasized.

Suggested Citation

  • Timothy P. Hubbard & Rene Kirkegaard, 2015. "Asymmetric Auctions with More Than Two Bidders," Working Papers 1502, University of Guelph, Department of Economics and Finance.
  • Handle: RePEc:gue:guelph:2015-02
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    File URL: http://www.uoguelph.ca/economics/repec/workingpapers/2015/2015-02.pdf
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    References listed on IDEAS

    as
    1. De Silva, Dakshina G. & Hubbard, Timothy P. & Kosmopoulou, Georgia, 2013. "Efficacy of a Bidder Training Program: Lessons from LINC," MPRA Paper 51329, University Library of Munich, Germany.
    2. Paarsch, Harry J., 1992. "Deciding between the common and private value paradigms in empirical models of auctions," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 191-215.
    3. Quang Vuong & Sandra Campo & Isabelle Perrigne, 2003. "Asymmetry in first-price auctions with affiliated private values," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(2), pages 179-207.
    4. Lamy, Laurent, 2012. "The econometrics of auctions with asymmetric anonymous bidders," Journal of Econometrics, Elsevier, vol. 167(1), pages 113-132.
    5. Dakshina G. De Silva & Timothy Dunne & Georgia Kosmopoulou, 2003. "An Empirical Analysis of Entrant and Incumbent Bidding in Road Construction Auctions," Journal of Industrial Economics, Wiley Blackwell, vol. 51(3), pages 295-316, September.
    6. Marion, Justin, 2007. "Are bid preferences benign? The effect of small business subsidies in highway procurement auctions," Journal of Public Economics, Elsevier, vol. 91(7-8), pages 1591-1624, August.
    7. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," Review of Economic Studies, Oxford University Press, vol. 67(3), pages 413-438.
    8. Kirkegaard, René, 2013. "Handicaps in incomplete information all-pay auctions with a diverse set of bidders," European Economic Review, Elsevier, vol. 64(C), pages 98-110.
    9. Véronique Flambard & Isabelle Perrigne, 2006. "Asymmetry in Procurement Auctions: Evidence from Snow Removal Contracts," Economic Journal, Royal Economic Society, vol. 116(514), pages 1014-1036, October.
    10. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    11. Timothy Hubbard & René Kirkegaard & Harry Paarsch, 2013. "Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 241-266, August.
    12. Li, Huagang & Riley, John G., 2007. "Auction choice," International Journal of Industrial Organization, Elsevier, vol. 25(6), pages 1269-1298, December.
    13. Hubbard, Timothy P. & Paarsch, Harry J., 2009. "Investigating bid preferences at low-price, sealed-bid auctions with endogenous participation," International Journal of Industrial Organization, Elsevier, vol. 27(1), pages 1-14, January.
    14. Timothy P. Hubbard & Harry J. Paarsch, 2012. "On the Numerical Solution of Equilibria in Auction Models with Asymmetries within the Private-Values Paradigm," Carlo Alberto Notebooks 291, Collegio Carlo Alberto.
    15. Parreiras, Sérgio O. & Rubinchik, Anna, 2010. "Contests with three or more heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 68(2), pages 703-715, March.
    16. Donald, Stephen G. & Paarsch, Harry J., 1996. "Identification, Estimation, and Testing in Parametric Empirical Models of Auctions within the Independent Private Values Paradigm," Econometric Theory, Cambridge University Press, vol. 12(03), pages 517-567, August.
    17. Todd Kaplan & Shmuel Zamir, 2012. "Asymmetric first-price auctions with uniform distributions: analytic solutions to the general case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 269-302, June.
    18. Lamy, Laurent, 2012. "The econometrics of auctions with asymmetric anonymous bidders," Journal of Econometrics, Elsevier, vol. 167(1), pages 113-132.
    19. Kirkegaard, René, 2009. "Asymmetric first price auctions," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1617-1635, July.
    20. René Kirkegaard, 2012. "A Mechanism Design Approach to Ranking Asymmetric Auctions," Econometrica, Econometric Society, vol. 80(5), pages 2349-2364, September.
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    More about this item

    Keywords

    Asymmetric Auctions; Boundary Conditions; First-Price Auctions;

    JEL classification:

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

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