A stability concept for matrix game optimal strategies and its application to linear programming sensitivity analysis |
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Authors: | Marvin D Troutt |
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Institution: | (1) Southern Illinois University at Carbondale, 62901, IL, USA |
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Abstract: | This paper studies a class of perturbations of a game matrix that alters each row by a different amount. We find that completely
mixed optimal strategies are stable under these perturbations provided the norm of the vector of additive amounts is sufficiently
small. Using this concept we give a new characterization of completely mixed grames. We also obtain a sensitivity result for
a class of perturbations of the technological coefficient matrix of positive linear programs. The stability of an optimal
strategy holds throughout at least a spherical neighborhood of the zero perturbation. We give a computational formula and
equivalent programming formulations for the radius of this neighborhood. |
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Keywords: | Matrix games row perturbations completely mixed games sensitivity analysis linear programming |
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