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First Price Auctions in the Asymmetric N Bidder Case

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Author Info
Lebrun, Bernard
Abstract

I consider the first price auction when the bidders' valuations may be differently distributed. I show that every Bayesian equilibrium is an "essentially" pure equilibrium formed by bid functions whose inverses are solutions of a system of differential equations with boundary conditions. I then prove the existence of an equilibrium. I prove its uniqueness when the valuation distributions have a mass point at the lower extremity of the support. I give sufficient conditions for uniqueness when every valuation distribution is one of two atomless distributions. I establish inequalities between equilibrium strategies when relations of stochastic dominance exist between valuation distributions. Copyright 1999 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

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Article provided by Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association in its journal International Economic Review.

Volume (Year): 40 (1999)
Issue (Month): 1 (February)
Pages: 125-42
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Handle: RePEc:ier:iecrev:v:40:y:1999:i:1:p:125-42

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  1. Sudip Gupta, 2004. "Endogenous Asymmetry and Entry in Sequential Multi-Unit Auctions: Identification and Estimation," Econometric Society 2004 North American Summer Meetings 566, Econometric Society. [Downloadable!]
  2. Roberto Burguet & Martin Perry, 2007. "Bribery and Favoritism by Auctioneers in Sealed-Bid Auctions," Contributions to Theoretical Economics, Berkeley Electronic Press, vol. 7(1), pages 1219-1219. [Downloadable!] (restricted)
    Other versions:
  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. [Downloadable!]
  4. Lixin Ye, 2004. "Optimal Auctions with Endogenous Entry," Contributions to Theoretical Economics, Berkeley Electronic Press, vol. 4(1), pages 1158-1158. [Downloadable!] (restricted)
  5. Ed Hopkins, 2008. "Rank-Based Methods for the Analysis of Auctions," Levine's Bibliography 122247000000001900, UCLA Department of Economics. [Downloadable!]
  6. Elena Krasnokutskaya, 2004. "Identification and Estimation in Highway Procurement Auctions under Unobserved Auction Heterogeneity," PIER Working Paper Archive 05-006, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
  7. Harrison Cheng, 2005. "Ranking Sealed High-Bid and Open Asymmetric Auctions," IEPR Working Papers 05.26, Institute of Economic Policy Research (IEPR). [Downloadable!]
  8. Ed Hopkins & Tatiana Kornienko, 2004. "Running to Keep in the Same Place: Consumer Choice as a Game of Status," ESE Discussion Papers 92, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  9. Todd R. Kaplan & Shmuel Zamir, 2006. "Asymmetric Auctions: Analytic Solutions to the General Uniform Case," Levine's Bibliography 321307000000000410, UCLA Department of Economics. [Downloadable!]
  10. Leslie M. Marx & Robert C. Marshall, 2004. "Bidder Collusion," Econometric Society 2004 North American Winter Meetings 108, Econometric Society. [Downloadable!]
  11. Bernard Lebrun, 2006. "Auctions with Almost Homogeneous Bidders," Working Papers 2006_7, York University, Department of Economics. [Downloadable!]
  12. Ed Hopkins, 2007. "Rank-Based Methods for the Analysis of Auctions," ESE Discussion Papers 173, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
  13. Rene Kirkegaard, 2005. "A Simple Approach to Analyzing Asymmetric First Price Auctions," Working Papers 0504, Brock University, Department of Economics, revised Nov 2005. [Downloadable!]
  14. Lescourret, Laurence & Robert, Christian Y., 2006. "Preferencing, internalization and inventory position," ESSEC Working Papers DR 06017, ESSEC Research Center, ESSEC Business School. [Downloadable!]
  15. Irene Martínez-Pardina, 2006. "First-price auctions where one of the bidders’ valuations is common knowledge," Review of Economic Design, Springer, vol. 10(1), pages 31-51, April. [Downloadable!] (restricted)
  16. Harry J. Paarsch & Bjarne Brendstrup, 2004. "Nonparametric Estimation of Dutch and First-Price, Sealed-Bid Auction Models with Asymmetric Bidders," Econometric Society 2004 North American Summer Meetings 39, Econometric Society. [Downloadable!]
  17. Harry J. Paarsch & Bjarne Brentstrup, 2004. "Nonparametric Identification and Estimation of Multi-Unit, Sequential, Oral, Ascending-Price Auctions with Asymmetric Bidders," Computing in Economics and Finance 2004 36, Society for Computational Economics. [Downloadable!]
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  18. Andreas Blume & Paul Heidhues, 2003. "Private Monitoring in Auctions," CIG Working Papers SP II 2003-14, Wissenschaftszentrum Berlin (WZB), Research Unit: Competition and Innovation (CIG). [Downloadable!]
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