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Bilateral Approach to the Secretary Problem


  • David M., Ramsey
  • Krzysztof, Szajowski


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 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.

Suggested Citation

  • David M., Ramsey & Krzysztof, Szajowski, 2000. "Bilateral Approach to the Secretary Problem," MPRA Paper 19888, University Library of Munich, Germany, revised 2003.
  • Handle: RePEc:pra:mprapa:19888

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    References listed on IDEAS

    1. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    2. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    3. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
    4. Perlin, M., 2007. "M of a kind: A Multivariate Approach at Pairs Trading," MPRA Paper 8309, University Library of Munich, Germany.
    5. K. Triantafyllopoulos & G. Montana, 2011. "Dynamic modeling of mean-reverting spreads for statistical arbitrage," Computational Management Science, Springer, vol. 8(1), pages 23-49, April.
    6. Perlin, M., 2007. "Evaluation of pairs trading strategy at the Brazilian financial market," MPRA Paper 8308, University Library of Munich, Germany.
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    Cited by:

    1. Ramsey, David M. & Szajowski, Krzysztof, 2004. "Correlated equilibria in competitive staff selection problem," MPRA Paper 19870, University Library of Munich, Germany, revised 2006.

    More about this item


    optimal stopping problem; game variant; Markov process; random priority; secretary problem;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory


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