Hostname: page-component-cb9f654ff-fg9bn Total loading time: 0 Render date: 2025-08-22T21:28:40.867Z Has data issue: false hasContentIssue false
  • English
  • Français

Reducing two person, zero sum games with underlying symmetry

Published online by Cambridge University Press:  09 April 2009

K. R. Pearson
K. R. Pearson
Affiliation:
Department of Mathematics La Trobe UniversityBundoora, Victoria 3083, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider two person, zero sum games with several symmetries. Where such symmetries are present there is a group acting on the strategies of the game. We show how to use this action to produce a reduced game with a smaller matrix, but having the same value as the original game, and how to obtain optimal strategies for the original game from optimal strategies of the reduced game. An analysis of a simplified version of the popular game Mastermind is given to illustrate the theory developed.

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 152 - 161
Copyright
Copyright © Australian Mathematical Society 1982

References

Gale, D., Kuhn, H. W. and Tucker, A. W. (1950), ‘Reduction of game matrices’, Contributions to the theory of games, vol. 1, pp. 89–96 (Ann. of Math. Studies, no. 24, Princeton Univ. Press, Princeton, N.J.).Google Scholar
Lane, S. Mac and Birkhoff, G. (1979), Algebra (2nd edition, Macmillan, New York).Google Scholar
Williams, J. D. (1966), The compleat strategyst (McGraw-Hill, New York).Google Scholar