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Solving a Matrix Game by Linear Programming

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1 Author(s)

This paper presents (1) a new characterization, via linear programming, of extreme optimal strategies of a matrix game and (2) a simple direct procedure for computing them. The first pertains to the neat formulas of L. S. Shapley and R. N. Snow for a “basic solution”, and the second to the highly effective “simplex method” of G. B. Dantzig. Both are related to the author's “combinational equivalence” of matrices, the first through an optimal block-pivot transformation and the second through a suitably chosen succession of elementary pivot steps.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:4 ,  Issue: 5 )

Date of Publication:

Nov. 1960

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