Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T17:24:31.151Z Has data issue: false hasContentIssue false
  • English
  • Français

Adaptive approach to some stopping problems

Published online by Cambridge University Press:  14 July 2016

Mitsushi Tamaki
Mitsushi Tamaki*
Affiliation:
Otemon-Gakuin University
*
∗Postal address: School of Economics, Otemon-Gakuin University, Nishiai, Ibaraki-city, Osaka, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper mainly considers the adaptive version of two typical stopping problems, i.e., the parking problem and the secretary problem with refusal. In the first problem, while driving towards a destination, we observe the successive parking places and note whether or not they are occupied. Unoccupied spaces are assumed to occur independently, with probability p. The second problem is to select the best applicant from a population, where each applicant refuses an offer with probability 1 – p. We assume beta prior for p in advance. As time progresses, we update our belief for p in a Bayesian manner based on the observed states of the process. We derive several monotonicity properties of the value function and characterize the optimal strategy in either problem. We also attempt to relax the same probability condition in the classical parking problem.

Keywords

OPTIMAL STOPPING PROBLEMPARKING PROBLEMSECRETARY PROBLEMDYNAMIC PROGRAMMINGBAYESIAN ANALYSIS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 644 - 652
Copyright
Copyright © Applied Probability Trust 1985 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Degroot, M. H. (1970) Optimal Statistical Decisions. McGraw-Hill, New York.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco, CA.Google Scholar
Smith, M. H. (1975) A secretary problem with uncertain employment. J. Appl. Prob. 12, 620–624.Google Scholar
Tamaki, M. (1979) Recognizing both the maximum and the second maximum of a sequence. J. Appl. Prob. 16, 803–812.Google Scholar
Tamaki, M. (1982) An optimal parking problem. J. Appl. Prob. 19, 803–814.Google Scholar