The postdoc variant of the secretary problem

Rober J. Vanderbei

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The classical secretary problem involves sequentially interviewing a pool of n applicants with the aim of hiring exactly the best one in the pool-nothing less is good enough. The optimal decision strategy is easy to describe and the probability of success is 1/e. In this paper, we consider a minor variant of this classical problem. We wish to pick not the best, but the second best (the best is going to Harvard). In this case, an explicit solution can be given both for the optimal strategy and the associated optimal success probability. The probability of success is k0(n-k0)/(n(n-1)) where k0= [n/2]. Clearly, as n goes to infinity, the probability of success tends to 1/4. Apparently, it is easier to pick the best than the second best.

Original languageEnglish (US)
Pages (from-to)3-13
Number of pages11
JournalMathematica Applicanda
Issue number1
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Decision Sciences (miscellaneous)


  • Online auctions
  • Online learning
  • Optimal stopping
  • Secretary problem


Dive into the research topics of 'The postdoc variant of the secretary problem'. Together they form a unique fingerprint.

Cite this