A STUDY OF PURE DOMINANCE AND MIXED DOMINANCE IN DECISION MATRICES.
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Title
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A STUDY OF PURE DOMINANCE AND MIXED DOMINANCE IN DECISION MATRICES.
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Identifier
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AAI8319781
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identifier
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8319781
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Creator
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LU, CHUNG KUT.
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Contributor
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Prof. George Sphicas
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Date
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1983
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Language
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English
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Publisher
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City University of New York.
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Subject
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Business Administration, Management
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Abstract
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In decision matrices, it is possible to classify the strategies in the matrices into three distinct classes, namely, (1) purely dominated strategies, (2) mixed dominated strategies, and (3) non-dominated strategies. The number of strategies in each class provides an important indication of the extent of presence of dominance and thus the reduction in size that can be achieved by eliminating dominated strategies. Knowledge of the expected values of the number of strategies that are purely dominated and mixed dominated in a given matrix can provide us information about the extent of dominated strategies that can be eliminated.;For small matrices, this study derives the analytical solutions for the expected values of pure dominance, mixed dominance and non-dominance for matrices with entries that are continuously distributed random variables of, (1) uniform distribution, (2) left-skewed triangular distribution, and (3) right-skewed triangular distribution. For larger matrices, simulation is used to estimate the expected values of pure dominance, mixed dominance and non-dominance for matrices with entries of the above three distributions and also of normal distribution. Based on the results obtained from the simulation, regression analysis is then applied to provide further estimates on the expected values on dominance for matrices not covered by the simulation.;Analysis in this study shows that for a given matrix with entries that are continuously distributed, the expected value of pure dominance depends only on n, the total number of strategies, and m, the total number of columns in the matrix, and is independent of the class of continuous distribution of the entries.;However, the expected values of mixed dominance in a given matrix also depends on the joint density functions of the entries in the associated game matrix. Difference in means and variances of the same distribution in the entries will not affect the expected value of mixed dominance for a given nxm matrix, as long as the distribution of the entries are standardizable.;The study concludes that the expected values of mixed dominance are highly significant when compared to both the expected values of pure dominance and non-dominance.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
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Program
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Business
