Improving a Cheating Applicant's Chances in the Secretary Problem
Abstract
The Secretary Problem (SP) is an abstraction of an optimal stopping problem often framed as a decision maker (DM) choosing from a queue of applicants. The "applicants" may represent interviewees, prospective spouses, sensor readings, food sources, or military targets. In its simplest form, a decision maker observes applicants one at a time and must choose a point at which to select a single applicant based only on the relative ranks of the applicants observed up to that point; payoff may be based on maximizing the probability of selecting the best applicant or minimizing the expected rank of the selected applicant. This paper develops methods for a cheating applicant to find advantageous positions in the queue that either improve the applicants probability of being selected or aid in evading selection. A variant of the SP is explored that allows for non-selection of a poor applicant. It is demonstrated that a statistical test of hypothesis is ineffective for detecting this means of deception, so the advantage is on the side of the cheating applicant.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 2019
- Accession Number
- AD1083923
Entities
People
- Warren H. Jr Debany
Organizations
- Air Force Research Laboratory