Summary The development of what has come to be known as the secretary problem is traced from its origins in the early 1960's. All published work to date on the problem and its extensions is reviewed.

The Secretary Problem and its Extensions: A Review

Sequential decision making with relative ranks: An experimental investigation of the "secretary problem."

We consider a class of sequential observation and selection decision problems in which applicants are interviewed one at a time, decision makers only learn the applicant's quality relative to the applicants that have been interviewed and rejected, only a single applicant is selected, and payoffs increase in the absolute quality of the selected applicant. Compared to the optimal decision policy, which we compute numerically, results from two experiments show that subjects terminated their search too early. We competitively test three behavioral decision rules and find that a multithreshold rule, which has the same form as the optimal decision policy but is parameterized differently, best accounts for the data. Results from a probability estimation task show that subjects tend to overestimate the absolute quality of early applicants and give insufficient consideration to the yet-to-be-seen applicants.

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Sequential Observation and Selection with Rank-Dependent Payoffs: An Experimental Study

This paper explores best choice problems which allow both recall of applicants and uncertainty of a current applicant accepting an offer of employment. Properties of optimal selection procedures are derived for the general case. Optimal procedures and the associated probabilities of obtaining the best applicant are found in two special cases. The results unify and extend those of Yang (1974) and Smith (1975). OPTIMAL STOPPING; SECRETARY PROBLEM: RELATIVE RANKS

Best-choice problems involving uncertainty of selection and recall of observations

Partial-order analogue of the secretary problem: the binary tree case

A ‘Secretary Problem’ with no recall but which allows the applicant to refuse an offer of employment with a fixed probability 1 – p, (0 < p < 1), is considered. The optimal stopping rule and the maximum probability of employing the best applicant are derived.

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M. H. Smith

Papers

A secretary problem with uncertain employment