The Annals of Probability

A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options

F. Thomas Bruss

Full-text: Open access

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.

Article information

Source
Ann. Probab. Volume 12, Number 3 (1984), 882-889.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176993237

Digital Object Identifier
doi:10.1214/aop/1176993237

Mathematical Reviews number (MathSciNet)
MR744243

Zentralblatt MATH identifier
0553.60047

JSTOR
links.jstor.org

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Best choice problem secretary problem optimal stopping time two person game

Citation

Bruss, F. Thomas. A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options. Ann. Probab. 12 (1984), no. 3, 882--889. doi:10.1214/aop/1176993237. http://projecteuclid.org/euclid.aop/1176993237.


Export citation