Bilateral approach to the secretary problem

Abstract

A mathematical model of competitive selection of the applicants for a post is considered. There are N applicants with similar qualifications on an interview list. The applicants come in random order and their salary demands are distinct. Two managers, I and II, interview them one at a time. The aim of the manager is to obtain the applicant who demands minimal salary. When both managers want to accept the same candidate, then some rule of assignment to one of the managers is applied. Any candidate hired by a manager will accept the offer with some given probability. A candidate can be hired only at the moment of his appearance and can be accepted at that moment. At each moment n one candidate is presented. The considered problem is a generalization of the best choice problem with uncertain employment and its game version with priority or random priority. The general stopping game model is constructed. The algorithms of construction of the game value and the equilibrium strategies are given. An example is solved.