ON A GENERALIZATION OF THE SECRETARY PROBLEM WITH UNCERTAIN SELECTION
Mitsushi Tamaki, Katsuhisa Ohno · Journal of the Operations Research Society of Japan · 2000
The secretary problem with uncertain selection, considered by Smith, is generalized to allow for the rejection probability to be rank-dependent. That is, if an offer of employment is given to the j-th best applicant, she rejects it with probability q_j, 1 __- q_3, while as n gets large there appears a time interval such that the optimal policy makes an offer alternately to relatively best applicants that appear on that interval if q_2 __- q_2 >__- ・・・ >__- q_n, which reflects the real world in the sense that the better the applicant is, the most likely it seems that she refuses an offer with the larger probability.