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

Mitchell Watt

doi:10.1016/j.econlet.2025.112628

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

Mitchell Watt

Department of Economics

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

I show that the expected k^th-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.

Original language	English
Article number	112628
Number of pages	4
Journal	Economics Letters
Volume	256
DOIs	https://doi.org/10.1016/j.econlet.2025.112628
Publication status	Published - Oct 2025

Keywords

Auctions
Concavity
Marketing costs
Order statistics

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10.1016/j.econlet.2025.112628Licence: CC BY

731889835-oaFinal published version, 590 KBLicence: CC BY

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title = "Concavity of order statistics in sample size: implications for auction design",

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.",

keywords = "Auctions, Concavity, Marketing costs, Order statistics",

author = "Mitchell Watt",

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journal = "Economics Letters",

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AB - 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.

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KW - Concavity

KW - Marketing costs

KW - Order statistics

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DO - 10.1016/j.econlet.2025.112628

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AN - SCOPUS:105016799102

SN - 0165-1765

VL - 256

JO - Economics Letters

JF - Economics Letters

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ER -

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

Abstract

Keywords

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