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Title: Optional stopping behavior with relative ranks : the secretary problem with unknown population size
Authors: Seale, Darryl A.
Rapoport, Amnon
Keywords: Optional stopping
Secretary problem
Relative ranks
Computer-controlled experiment
Optimal policy
Optimal selection
Search cost
Issue Date: Sep-1997
Series/Report no.: Marketing Working Paper Series ; MKTG 97.102
Abstract: We examine multi-period observation and selection problems with an unknown number of applicants in which applicants are interviewed one at a time on each period, recall of applicants that were interviewed and rejected is not possible, the decision on each period to reject or accept an applicant is based on relative ranks, and the objective is to maximize the probability of accepting the top ranked applicant. Having assessed the efficiency of three simple decision rules by simulation, we then test them competitively in a computer-controlled experiment. A cutoff decision rule, in which the first r - 1 applicants are rejected and then the first applicant who is ranked high than all previously observed applicants is accepted, outperforms the two other decision rules. Compared to the optimal policy, which uses the same cutoff decision rule, subjects stop the search too early. This behavior is accounted for by a model postulating an endogenous cost of search.
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