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Decreasing Returns to Sampling Without Replacement

Author

Listed:
  • David Ronayne

    (ESMT Berlin)

  • David P. Myatt

    (London Business School)

Abstract

We study sampling from a finite population without replacement when seeking an extreme (lowest or highest) value. An example is a buyer searching for the lowest price. It is well known that there are decreasing returns to sampling from continuous populations: the expected minimum is a decreasing and discretely convex function of the sample size. We show that is true for sampling without replacement from a finite population. We also give a simple sufficient condition on population values for the properties to hold for other order statistics.

Suggested Citation

  • David Ronayne & David P. Myatt, 2025. "Decreasing Returns to Sampling Without Replacement," Rationality and Competition Discussion Paper Series 555, CRC TRR 190 Rationality and Competition.
    • Handle: RePEc:rco:dpaper:555
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    References listed on IDEAS

    as
    1. Diane L. Evans & Lawrence M. Leemis & John H. Drew, 2006. "The Distribution of Order Statistics for Discrete Random Variables with Applications to Bootstrapping," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 19-30, February.
    2. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-969, July.
    3. José Luis Moraga‐González & Zsolt Sándor & Matthijs R. Wildenbeest, 2013. "Semi‐Nonparametric Estimation Of Consumer Search Costs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1205-1223, November.
    4. Michael R. Baye & John Morgan & Patrick Scholten, 2004. "Price Dispersion In The Small And In The Large: Evidence From An Internet Price Comparison Site," Journal of Industrial Economics, Wiley Blackwell, vol. 52(4), pages 463-496, December.
    5. David P. Myatt & David Ronayne, 2025. "Finding a Good Deal: Stable Prices, Costly Search, and the Effect of Entry," Rationality and Competition Discussion Paper Series 524, CRC TRR 190 Rationality and Competition.
    6. Watt, Mitchell, 2025. "Concavity of order statistics in sample size: Implications for auction design," Economics Letters, Elsevier, vol. 256(C).
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