A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals

  • Mitsushi TamakiEmail author
  • Qi Wang
Part of the Springer Optimization and Its Applications book series (SOIA, volume 39)


Suppose that a random number N of rankable applicants appear and their arrival times are i.i.d. random variables having a known distribution function. A method of choosing the best applicant is investigated when a prior on N is uniform on \(\{1,2,\ldots ,n\}\). An exact form of the optimal selection rule is derived. Stewart first studied this problem, but examined only the case of the non-informative prior, i.e., the limiting case of \(n\to \infty\), so our result can be considered as a generalization of Stewart’s result.


secretary problem optimal stopping bayesian updating OLA rule \(e^{-1}\)-rule relative rank 



We are grateful to the anonymous referees for their careful reading.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Business AdministrationAichi UniversityAichiJapan

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