Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T16:31:29.511Z Has data issue: false hasContentIssue false
  • English
  • Français

Sequential games

Part of: Decision theory Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Kyle Siegrist  and
John Steele
Kyle Siegrist*
Affiliation:
University of Alabama in Huntsville
John Steele*
Affiliation:
University of Alabama in Huntsville
*
∗ Postal address: Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA.
∗ Postal address: Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a general construction of sequential games among multiple players, as well as a construction of the composition of sequential games. We obtain new properties of the optimal class of win-by-k games, including closure under composition and independence between the winner of the game and the number of points played. We obtain new results on the asymptotic efficiency of the n-point, win-by-k games.

Keywords

Sequential gamecompositioncoherenceirrelevant pointindependence propertyefficiencywin-by-k game

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62C05: General considerations 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 4 , December 2001 , pp. 1006 - 1017
Copyright
Copyright © by the Applied Probability Trust 2001 

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

Anderson, K., Sobel, M., and Uppuluri, V. (1982). Quota fulfillment times. Canad. J. Statist. 10, 73–88.Google Scholar
Barlow, R. (1988). Engineering Reliability. SIAM, New York.Google Scholar
Barlow, R., and Proschan, F. (1965). Mathematical Theory of Reliability. John Wiley, New York.Google Scholar
DeCani, J. (1971). On the number of replications of a paired comparison. Biometrika 58, 169–175.Google Scholar
Feller, W. (1968). An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edn. John Wiley, New York.Google Scholar
Govindarajulu, Z. (1975). Sequential Statistical Procedures. Academic Press, New York.Google Scholar
Haigh, J. (1996). More on n-point, win-by-k games. J. Appl. Prob. 33, 382–387.Google Scholar
Hald, A. (1990). A History of Probability and Statistics and Their Applications before 1750. John Wiley, New York.Google Scholar
Johnson, N., Kotz, S., and Kemp, A. (1992). Univariate Discrete Distributions, 2nd edn. John Wiley, New York.Google Scholar
Maisel, H. (1996). Best k of 2k-1 comparisons. J. Amer. Statist. Assoc. 61, 329–344.Google Scholar
Menon, V., and Indira, N. (1983). On the asymptotic normality of the number of replications of a paired comparison. J. Appl. Prob. 20, 554–562.Google Scholar
Miles, R. (1984). Symmetric sequential analysis: the efficiencies of sports scoring systems (with particular reference to those of tennis). J. R. Statist. Soc. B 46, 93–108.Google Scholar
Miles, R. (1988). Scoring systems in sports. In Encyclopedia of Statistical Science, Vol. 8, eds Kotz, S. and Johnson, N., John Wiley, New York, pp. 607–609.Google Scholar
Morris, C. (1977). The most important points in tennis. In Optimal Strategies in Sports, eds Ladany, S. and Machol, R., North Holland, Amsterdam.Google Scholar
Pollard, G. (1983). An analysis of classical and tie-breaker tennis. Austral. J. Statist. 25, 496–505.Google Scholar
Pollard, G. (1990). A method for determining the asymptotic efficiency of some sequential probability ratio tests. Austral. J. Statist. 32, 191–204.CrossRefGoogle Scholar
Ross, S. (1996). Stochastic Processes, 2nd edn. John Wiley, New York.Google Scholar
Siegrist, K. (1989). n-point, win-by-k games. J. Appl. Prob. 27, 804–814.Google Scholar
Uppuluri, V., and Blot, W. (1974). Asymptotic properties of the number of replications of a paired comparison. J. Appl. Prob. 11, 43–52.CrossRefGoogle Scholar
Wald, A. (1947). Sequential Analysis. John Wiley, New York.Google Scholar