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Bidding against an unknown number of competitiors sharing affiliated information

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  • Vleugels, Jan

    () (University Mannheim)

Abstract

In the general symmetric model of Milgrom and Weber, equilibrium bidding is analyzed with a stochastic number of bidders. the equilibrium strategies generalize the known expressions in a coherent way. For the equilibrium bid function of the first price auction, an interpretation involving 'marginal winning probabilities' is proposed. With ageneralized version of the linkage principle, the well-knownrevenue ranking theorems extend to a stochastic number of bidders. As an application, we show that the seller's generically optimal information policy regarding the number of competitors is concealing the information.

Suggested Citation

  • Vleugels, Jan, 1997. "Bidding against an unknown number of competitiors sharing affiliated information," Sonderforschungsbereich 504 Publications 97-13, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  • Handle: RePEc:xrs:sfbmaa:97-13
    Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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    File URL: http://www.sfb504.uni-mannheim.de/publications/dp97-13.pdf
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    References listed on IDEAS

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    1. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
    2. Wilson, Robert, 1992. "Strategic analysis of auctions," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 8, pages 227-279 Elsevier.
    3. Harstad, Ronald M. & Kagel, John H. & Levin, Dan, 1990. "Equilibrium bid functions for auctions with an uncertain number of bidders," Economics Letters, Elsevier, vol. 33(1), pages 35-40, May.
    4. French, Kenneth R & McCormick, Robert E, 1984. "Sealed Bids, Sunk Costs, and the Process of Competition," The Journal of Business, University of Chicago Press, vol. 57(4), pages 417-441, October.
    5. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    6. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    7. Ronald M. Harstad & Dan Levin, 1985. "A Class of Dominance Solvable Common-Value Auctions," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 525-528.
    8. Smith, James L. & Levin, Dan, 1996. "Ranking Auctions with Risk Averse Bidders," Journal of Economic Theory, Elsevier, vol. 68(2), pages 549-561, February.
    9. Harstad, Ronald M, 1990. "Alternative Common-Value Auction Procedures: Revenue Comparisons with Free Entry," Journal of Political Economy, University of Chicago Press, vol. 98(2), pages 421-429, April.
    10. Robert Wilson, 1977. "A Bidding Model of Perfect Competition," Review of Economic Studies, Oxford University Press, vol. 44(3), pages 511-518.
    11. Burguet, Roberto & Sakovics, Jozsef, 1996. "Reserve Prices without Commitment," Games and Economic Behavior, Elsevier, vol. 15(2), pages 149-164, August.
    12. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    13. Levin, Dan & Smith, James L, 1994. "Equilibrium in Auctions with Entry," American Economic Review, American Economic Association, vol. 84(3), pages 585-599, June.
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