Secretary Problems with Competing Employers

  • Nicole Immorlica
  • Robert Kleinberg
  • Mohammad Mahdian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


In many decentralized labor markets, job candidates are offered positions at very early stages in the hiring process. It has been argued that these early offers are an effect of the competition between employers for the best candidate. This work studies the timing of offers in a theoretical model based on the classical secretary problem. We consider a secretary problem with multiple employers and study the equilibria of the induced game. Our results confirm the observation of early offers in labor markets: for several classes of strategies based on optimal stopping theory, as the number of employers grows, the timing of the earliest offer decreases.


Nash Equilibrium Active Player Stochastic Game Threshold Time Pure Nash Equilibrium 
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  1. 1.
    Dynkin, E.B.: The optimum choice of the instant for stopping a markov process. Sov. Math. Dokl. 4 (1963)Google Scholar
  2. 2.
    Ajtai, M., Megiddo, N., Waarts, O.: Improved algorithms and analysis for secretary problems and generalizations. SIAM J. Discrete Math. 14, 1–27 (2001)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Freeman, P.: The secretary problem and its extensions: a review. Internat. Statist. Rev. 51, 189–206 (1983)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gilbert, J.P., Mosteller, F.: Recognizing the maximum of a sequence. J. Amer. Statist. Assoc. 61, 35–73 (1966)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Sakaguchi, M.: Optimal stopping games: A review. Math. Japonica 42, 343–351 (1995)MATHMathSciNetGoogle Scholar
  6. 6.
    Dynkin, E.: Game variant of a problem on optimal stopping. Sov. Math. Dokl. 10, 270–274 (1969)MATHGoogle Scholar
  7. 7.
    Szajowski, K.: Double stopping by two decision-makers. Adv. in Appl. Probab. 25, 438–452 (1993)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Szajowski, K.: Optimal stopping of a discrete markov process by two decision makers. SIAM J. Control Optim. 33, 1392–1410 (1995)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Fushimi, M.: Secretary problem in a competitive situation. Journal of the Operations Research Society of Japan 24, 350–358 (1981)MATHMathSciNetGoogle Scholar
  10. 10.
    Ravindran, G., Szajowski, K.: Nonzero sum game with priority as Dynkin’s game. Math. Japonica 37, 401–413 (1992)MATHMathSciNetGoogle Scholar
  11. 11.
    Szajowski, K.: On nonzero sum game with priority in the secretary problem. Math. Japon. 37, 415–426 (1992)MATHMathSciNetGoogle Scholar
  12. 12.
    Szajowski, K.: Markov stopping games with random priority. Z. Oper. Res. 39, 69–84 (1994)MATHMathSciNetGoogle Scholar
  13. 13.
    Avery, C., Jolls, C., Posner, R., Roth, A.: The market for federal judicial law clerks. University of Chicago Law Review 68, 793–902 (2001)CrossRefGoogle Scholar
  14. 14.
    Roth, A., Xing, X.: Jumping the gun: Imperfections and institutions related to the timing of market transactions. American Economic Review 84, 992–1044 (1994)Google Scholar
  15. 15.
    Billingsley, P.: Probability and Measure. John Wiley, Chichester (1995)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nicole Immorlica
    • 1
  • Robert Kleinberg
    • 2
  • Mohammad Mahdian
    • 1
  1. 1.Microsoft ResearchOne Microsoft WayRedmond
  2. 2.UC Berkeley Computer Science DivisionCornell University Computer Science Department 

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