J. Neil Bearden
Associate Professor of Decision Sciences
Optimal stopping; Sequential search; Secretary problem;
The author presents an extension of the secretary problem in which the decision maker (DM) sequentially observes up to n applicants whose values are random variables X1,X2,…,XnX1,X2,…,Xn drawn i.i.d. from a uniform distribution on [0,1][0,1].The DM must select exactly one applicant, cannot recall released applicants, and receives a payoff of xtxt, the realization of XtXt, for selecting the t th applicant. For each encountered applicant, the DM only learns whether the applicant is the best so far.The author proves that the optimal policy dictates skipping the first sqrt(nn)-1 applicants, and then selecting the next encountered applicant whose value is a maximum.