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A Combinatorial method for a class of matrix games

Published online by Cambridge University Press:  14 July 2016

Rodrigo A. Restrepo
Rodrigo A. Restrepo*
Affiliation:
University of British Columbia
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The optimal strategies of any finite matrix game can be characterized by means of the Snow-Shapley Theorem [1]. However, in order to use this theorem to compute the optimal strategies, it may be necessary to invert a large number of matrices, most of which are not related to the solutions of the game. The present paper will show that when the columns of the pay-off matrix satisfy some special relations, it is possible to enumerate a much smaller class of matrices from which the optimal strategies may be obtained. Furthermore, the maximizing strategies that are determined by these matrices can be written down by inspection as soon as the matrices are specified.

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Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966, pp. 495 - 511
Copyright
Copyright © Applied Probability Trust 

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References

[1] Shapley, L. S. and Snow, R. N. (1950) Basic solutions of discrete games. Ann. Math. Stud. 24, 27–37.Google Scholar
[2] Cooper, J. N. and Restrepo, R. A. Some Problems of Attack and Defence (to be published).Google Scholar
[3] Dresher, M. (1951) Theory and Applications of Games of Strategy. The Rand Corporation R. 261, Santa Monica, Calif. Google Scholar
[4] Dresher, M. (1961) Games of Strategy: Theory and Applications. Prentice Hall. Inc., Englewood Clifis, N. J. Google Scholar
[5] Karlin, S. (1959) Mathematical Methods in the Theory of Games, Programming and Economics. Addison Wesley, Reading, Mass. Google Scholar