Optimizing a single uncertain selection by recall of observations

Abstract

This paper considers a variation of the classical secretary problem; this variation allows for the interviewer to make an offer to previously interviewed applicants and for the applicant to reject an offer. In this version, the process ends after any offer is made. Two special cases are considered, where the optimal procedure and its probability of success are given for each. Furthermore, the problem is discussed in general and conditions for optimal strategies are given.