Bilateral Approach to the Secretary Problem

Ramsey, David M. and Szajowski, Krzysztof (2000): Bilateral Approach to the Secretary Problem. Published in: Annals of the International Society of Dynamic Games , Vol. 7, (2005): pp. 271-284.

Abstract

A mathematical model of competitive selection of the applicants for a post is considered. There are N applicants of similar qualifications on an interview list. The applicants come in a random order and their salary demands are distinct. Two managers, I and II, will interview them one at a time. The aim of the manager is to obtain the applicant which demands minimal salary. The candidate can be accepted only at the moment of its appearance. When both manager want to accept the same candidate, then some rule of assignment to one of the manager is applied. Any candidate hired by the manager will accept the offer with some given probability. An candidate can be hired only at the moment of its appearance. At each moment n one candidate is presented. The considered problem is a generalisation of <i best choice problem></i> the best choice problem with uncertain employment and the game version of it 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: optimal stopping problem, game variant, Markov process, random priority, secretary problem
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

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