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A Note on Log Concave Survivor Functions in Auctions

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Abstract

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.

Suggested Citation

  • Seamus Hogan & Laura Meriluoto, 2010. "A Note on Log Concave Survivor Functions in Auctions," Working Papers in Economics 10/17, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:10/17
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/1017.pdf
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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    3. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
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    More about this item

    Keywords

    English Auction; Log Concavity; Survivor Function;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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