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August, 1984 A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options
F. Thomas Bruss
Ann. Probab. 12(3): 882-889 (August, 1984). DOI: 10.1214/aop/1176993237

Abstract

This article tries to unify best choice problems under total ignorance of both the candidates, quality distribution and the distribution of the number of candidates. The result is what we shall call the $e^{-1}$-law because of the multiple role which is played by $e^{-1}$, and this in a more general context as only in the solution of the classical secretary problem. The unification is possible whenever best choice problems can be redefined as continuous time decision problems on conditionally independent arrivals. We shall also give several examples to illustrate how the approach and its implications compare with other models.

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F. Thomas Bruss. "A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options." Ann. Probab. 12 (3) 882 - 889, August, 1984. https://doi.org/10.1214/aop/1176993237

Information

Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0553.60047
MathSciNet: MR744243
Digital Object Identifier: 10.1214/aop/1176993237

Subjects:
Primary: 60G40

Keywords: best choice problem , optimal stopping time , secretary problem , two person game

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 3 • August, 1984
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