Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T10:19:47.823Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

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.)

Footnotes

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

References

Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.Google Scholar
Elfving, G. (1967) A persistancy problem connected with a point process. J. Appl. Prob. 4, 77–89.Google Scholar
Enns, E. G. and Ferenstein, E. (1985) The horse game. J. Operat. Res. Soc. Japan 28, 51–62.Google Scholar
Enns, E. G. and Ferenstein, E. (1987) On a multi-person time-sequential game with priorities. Sequential Analysis 6, 239–256.Google Scholar
Enns, E. G., Ferenstein, E. and Sheahan, J. N. (1986) A curious recursion arising in game theory. Utilitas Math. 30, 219–228.Google Scholar
Flett, T. M. (1980) Differential Analysis. Cambridge University Press.Google Scholar
Presman, E. L. and Sonin, I. M. (1975) Equilibrium points in a game related to the best choice problem. Theory Prob. Appl. 20, 770–781.Google Scholar
Stadje, W. (1987) An optimal k-stopping problem for the Poisson process. In Mathematical Statistics and Probability Theory, Vol. B, ed. Bauer, P. et al., Reidel, Dordrecht, 231–244.Google Scholar