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A full-information best-choice problem with finite memory

Published online by Cambridge University Press:  14 July 2016

Mitsushi Tamaki
Mitsushi Tamaki*
Affiliation:
Otemon Gakuin University
*
∗Present address: Department of Law and Economics, Aichi University, Toyohashi-city, Aichi, Japan.
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Abstract

n i.i.d. random variables with known continuous distribution are observed sequentially with the objective of selecting the largest. This paper considers the finite-memory case which, at each stage, allows a solicitation of anyone of the last m observations as well as of the present one. If the (k – t)th observation with value x is solicited at the k th stage, the probability of successful solicitation is p1(x) or p2(x) according to whether t = 0 or 1 ≦ t ≦ m. The optimal procedure is shown to be characterized by the double sequences of decision numbers. A simple algorithm for calculating the decision numbers and the probability of selecting the largest is obtained in a special case.

Keywords

SECRETARY PROBLEMOPTIMAL STOPPING RULE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 718 - 735
Copyright
Copyright © Applied Probability Trust 1986 

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References

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