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Concavity of order statistics in sample size: Implications for auction design

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  • Watt, Mitchell

Abstract

I show that the expected kth-highest order statistic from a monotone hazard rate distribution is concave in sample size. In independent private value auctions with convex marketing costs, this ensures that the seller’s objective is concave, yielding a finite optimum.

Suggested Citation

  • Watt, Mitchell, 2025. "Concavity of order statistics in sample size: Implications for auction design," Economics Letters, Elsevier, vol. 256(C).
    • Handle: RePEc:eee:ecolet:v:256:y:2025:i:c:s0165176525004653
    DOI: 10.1016/j.econlet.2025.112628
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    References listed on IDEAS

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    1. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, Enero-Abr.
    2. David, H. A., 1997. "Augmented order statistics and the biasing effect of outliers," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 199-204, December.
    3. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    4. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    5. Ramesh Gupta & N. Balakrishnan, 2012. "Log-concavity and monotonicity of hazard and reversed hazard functions of univariate and multivariate skew-normal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 181-191, February.
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    Keywords

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    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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