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On the game of googol

International Journal of Game Theory volume 21, pages 151–160 (1992)Cite this article

Abstract

In the classical secretary problem the decision maker can only observe the relative ranks of the items presented. Recently, Ferguson — building on ideas of Stewart — showed that, in a game theoretic sense, there is no advantage if the actual values of the random variables underlying the relative ranks can be observed (game of googol). We extend this to the case where the number of items is unknown with a known upper bound. Corollary 3 extends one of the main results in [HK] toall randomized stopping times. We also include a modified, somewhat more formal argument for Ferguson's result.

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Author information

Authors and Affiliations

  1. Georgia Institute of Technology, School of Mathematics, 30332, Atlanta, GA, USA

    T. P. Hill

  2. Institut für Mathematische Stochastik, Lotzestraße 13, 3400, Göttingen

    U. Krengel

Authors
  1. T. P. Hill
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  2. U. Krengel
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Additional information

The first author was supported in part by NSF Grant DMS-89-01267.

This research was done during a visit of the second author at the Georgia Institute of Technology, Atlanta. This visit was supported by the Deutsche Forschungsgemeinschaft.

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Hill, T.P., Krengel, U. On the game of googol. Int J Game Theory 21, 151–160 (1992). https://doi.org/10.1007/BF01245458

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  • DOI: https://doi.org/10.1007/BF01245458

Keywords

  • Decision Maker
  • Economic Theory
  • Game Theory
  • Relative Rank
  • Formal Argument