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A competitive best-choice problem with Poisson arrivals

Published online by Cambridge University Press:  14 July 2016

E. G. Enns and
E. Z. Ferenstein
E. G. Enns*
Affiliation:
University of Calgary
E. Z. Ferenstein*
Affiliation:
Institute of Mathematics, Technical University of Warsaw
*
∗ Postal address: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, Canada T2N 1N4.
∗∗ Postal address: Institute of Mathematics, Technical University of Warsaw, Pl. Jedności Robotniczej 1, 00–661 Warsaw, Poland.
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Abstract

Two competitors observe a Poisson stream of offers. The offers are independent and identically distributed random variables from some continuous distribution. Each of the competitors wishes to accept one offer in the interval [0, T] and each aims to select an offer larger than that of his competitor. Offers are observed sequentially and decisions to accept or reject must be made when the offers arrive. Optimal strategies and winning probabilities are obtained for the competitors under a priorized decision scheme. The time of first offer acceptance is also analyzed. In all cases the asymptotic results are obtained.

Keywords

OPTIMAL STOPPING TIMESEQUENTIAL DECISIONS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990, pp. 333 - 342
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

The authors acknowledge the support of the National Science and Engineering Research Council of Canada.

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