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First Price Auctions in the Asymmetric N Bidder Case

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  • 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.

Suggested Citation

  • 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.
  • Handle: RePEc:ier:iecrev:v:40:y:1999:i:1:p:125-42
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