A Note on Log Concave Survivor Functions in Auctions
In a standard English auction in which bidders’ valuations are independently drawn from a common distribution, a standard regularity condition is that the survivor function of the distribution be log concave. In an auction where the seller sets a fixed price, the equivalent condition requires log concavity of a survivor function derived from the primitive distribution. In this note we show that log concavity of the primitive survivor function implies log concavity in the derived functions. This result is of interest when studying on-line auctions that combined aspects of fixed-price and English auctions.
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- Bagnoli, M. & Bergstrom, T., 1989.
"Log-Concave Probability And Its Applications,"
89-23, Michigan - Center for Research on Economic & Social Theory.
- Lebrun, Bernard, 2006.
"Uniqueness of the equilibrium in first-price auctions,"
Games and Economic Behavior,
Elsevier, vol. 55(1), pages 131-151, April.
- Bernard Lebrun, 2004. "Uniqueness of the Equilibrium in First-Price Auctions," Discussion Papers 1, York University, Department of Economics, revised May 2004.
- Bernard Lebrun, 2004. "Uniqueness of the Equilibrium in First-Price Auctions," Working Papers 2004_2, York University, Department of Economics.
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