A secretary problem with uncertain employment and restricted offering chances
Katsunori Ano, Mitsushi Tamaki · Institutional Repositories DataBase (IRDB) · 1992
A version of the secretary problem with no recall, in which an offer of acceptance is refused by the applicant with a fixed known probability $1-p,$ $(0\leq p\leq 1)$ and the offering chances, until the decision maker gets one applicant, are at most $M$ times is treated.This problem is an extension of Smith (1975).The optimal strategy of this problem is obtained in Section 2. In Section 3, as example,the optimal offering strategies and the maximum probabilities of selecting the best applicant are given for the problems with $M=1,2,3$ respectively.