A satisficing policy of the secretary problem: theory and simulation

In the standard secretary problem (SP), a decision-maker (DM) tries to choose the best applicant of a sequentially ordered set, and the goal is to maximize the probability of choosing the best applicant. In this paper, we extend the standard SP and present a satisficing policy. There are several satisfactory applicants for the DM to choose under the satisficing policy. The DM cannot rank all the applicants from best to worst due to the limits of the DM’s incomplete preferences, and the goal is to maximize the probability of choosing one of satisfactory applicants. For the secretary problem with 2 and 3 satisfactory applicants respectively, on the one hand, the asymptotic results of the maximum probability of choosing a satisfactory applicant and the corresponding optimal cutoff value are computed respectively. On the other hand, a series of computer simulations are conducted to estimate the optimal cutoff value and the maximum probability of choosing a satisfactory applicant. The effects of incorporating endogenous search cost in the case of 50 and 100 applicants are investigated respectively under the satisficing policy. The satisficing policy of this paper can be regarded as an extension of the optimal policy of the standard SP.