Recognizing the maximum of a random sequence based on relative rank with backward solicitation
Mark C. K. Yang · Journal of Applied Probability · 1974
The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.