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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
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Abstract

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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.

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

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