Abstract
In this paper, we propose new solution concepts for multicriteria games and compare them with existing ones. The general setting is that of two-person finite games in normal form (matrix games) with pure and mixed strategy sets for the players. The notions of efficiency (Pareto optimality), security levels, and response strategies have all been used in defining solutions ranging from equilibrium points to Pareto saddle points. Methods for obtaining strategies that yield Pareto security levels to the players or Pareto saddle points to the game, when they exist, are presented. Finally, we study games with more than two qualitative outcomes such as combat games. Using the notion of guaranteed outcomes, we obtain saddle-point solutions in mixed strategies for a number of cases. Examples illustrating the concepts, methods, and solutions are included.
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References
Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965.
Ardema, M. D., Heymann, M., andRajan, N.,Combat Games, Journal of Optimization Theory and Applications, Vol. 46, No. 4, pp. 391–398, 1985.
Prasad, U. R., andGhose, D.,Pareto-Optimality Concept Applied to Combat Games, 2nd International Symposium on Differential Game Applications, Williamsburg, Virginia, 1986.
Prasad, U. R., andGhose, D.,Formulation and Analysis of Combat Problems as Zero-Sum Bicriterion Differential Games, Journal of Optimization Theory and Applications, Vol. 59, No. 1, pp. 1–24, 1988.
Blackwell, D.,An Analog of the Minimax Theorem for Vector Payoffs, Pacific Journal of Mathematics, Vol. 6, No. 1, pp. 1–8, 1956.
Shapley, L. S.,Equilibrium Points in Games with Vector Payoffs, Naval Research Logistics Quarterly, Vol. 6, No. 1, pp. 57–61, 1959.
Nieuwenhuis, J. W.,Some Minimax Theorems in Vector-Valued Functions, Journal of Optimization Theory and Applications, Vol. 40, No. 3, pp. 463–475, 1983.
Corley, H. W.,Games with Vector Payoffs, Journal of Optimization Theory and Applications, Vol. 47, No. 4, pp. 491–498, 1985.
Leitmann, G.,Cooperative and Noncooperative Differential Games, Multicriteria Decision Making, Edited by G. Leitmann and A. Marzollo, Springer-Verlag, New York, New York, 1975.
Schmitendorf, W. E.,Optimal Control of Systems with Multiple Criteria When Disturbances Are Present, Journal of Optimization Theory and Applications, Vol. 27, No. 1, pp. 135–146, 1979.
Schmitendorf, W. E., andMoriarty, G.,A Sufficiency Condition for Coalitive Pareto-Optimal Solutions, Multicriteria Decision Making and Differential Games, Edited by G. Leitmann, Plenum Press, New York, New York, 1976.
Lin, J. G.,Maximal Vectors and Multi-Objective Optimization, Journal of Optimization Theory and Applications, Vol. 18, No. 1, pp. 41–64, 1976.
Arrow, K. J., Barankin, E. W., andBlackwell, D.,Admissible Points of Convex Sets, Contributions to the Theory of Games, II, Edited by H. W. Kuhn and A. W. Tucker, Princeton University Press, Princeton, New Jersey, 1953.
Shubik, M.,Game Theory in the Social Sciences, Concepts and Solutions, MIT Press, Cambridge, Massachusetts, 1982.
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Communicated by W. E. Schmitendorf
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Ghose, D., Prasad, U.R. Solution concepts in two-person multicriteria games. J Optim Theory Appl 63, 167–189 (1989). https://doi.org/10.1007/BF00939572
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DOI: https://doi.org/10.1007/BF00939572