Abstract
Two-person games are defined in which the payoffs are vectors. Necessary and sufficient conditions for optimal mixed strategies are developed, and examples are presented.
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References
Backwell, D.,An Analog of the Minimax Theorem for Vector Payoffs, Pacific Journal of Mathematics, Vol. 6, pp. 1–8, 1956.
Nieuwenhuis, J. W.,Some Minimax Theorems in Vector-Valued Functions, Journal of Optimization Theory and Applications, Vol. 40, pp. 463–475, 1983.
Corley, H. W.,Duality Theory for the Matrix Linear Programming Problem, Journal of Mathematical Analysis and Applications, Vol. 104, pp. 47–52, 1984.
Owen, G.,Game Theory, Academic Press, New York, New York, 1982.
Aubin, J. P.,Mathematical Methods of Games and Economic Behavior, North-Holland, Amsterdam, Holland, 1979.
Isermann, H.,Proper Efficiency and the Linear Vector Maximum Problem, Operations Research, Vol. 22, pp. 189–191, 1974.
Bazaraa, M. S., andShetty, C. M.,Nonlinear Programming: Theory and Algorithms, John Wiley, New York, New York, 1979.
Wolfe, P.,The Simplex Method for Quadratic Programming, Econometrica, Vol. 27, pp. 382–398, 1959.
Lemke, C. E., andHowson, J. T., Jr.,Equilibrium Points of Bimatrix Games, SIAM Journal on Applied Mathematics, Vol. 12, pp. 413–423, 1964.
Nash, J.,Noncooperative Games, Annals of Mathematics, Vol. 54, pp. 286–295, 1951.
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Communicated by P. L. Yu
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Corley, H.W. Games with vector payoffs. J Optim Theory Appl 47, 491–498 (1985). https://doi.org/10.1007/BF00942194
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DOI: https://doi.org/10.1007/BF00942194