The secretary problem with an unknown number of candidates
A. R. Abdel-hamid, J. A. Bather, G. B. Trustrum · Journal of Applied Probability · 1982
When the number of candidates is unknown, the problem of selecting the best during a sequence of interviews has many reasonable solutions. A simple condition for admissibility is established and it is shown that the class of Bayes solutions obtained by treating the number of candidates as a random variable is by no means complete. On the other hand, there is a single improper prior distribution for which the extended Bayes solutions constitute the whole family of admissible procedures.