Nondominated equilibrium solutions of multiobjective two-person nonzero-sum games in normal and extensive forms
作者： Ichiro Nishizaki
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摘要: In this paper, we review the development of studies on multiobjective noncooperative games, and particularly we focus on nondominated equilibrium solutions in two-person nonzero-sum games normal extensive forms. After outlining studies related to treat form, a mathematical programming problem yielding is shown. As for form first provide game representation sequence then formulate obtaining solutions.
okayama-u.ac.jp参考文章(28)
H. L. Le Roy, L. Lecam, J. Neyman, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability; Vol. IV Revue de l'Institut International de Statistique / Review of the International Statistical Institute. ,vol. 37, pp. 230- ,(1969) , 10.2307/1402306
Masatoshi Sakawa, Ichiro Nishizaki, Max-min solutions for fuzzy multiobjective matrix games Fuzzy Sets and Systems. ,vol. 67, pp. 53- 69 ,(1994) , 10.1016/0165-0114(94)90208-9
P. L. Yu, Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives Journal of Optimization Theory and Applications. ,vol. 14, pp. 319- 377 ,(1974) , 10.1007/BF00932614
S. Y. Wang, Existence of a Pareto equilibrium Journal of Optimization Theory and Applications. ,vol. 79, pp. 373- 384 ,(1993) , 10.1007/BF00940586
David Blackwell, An analog of the minimax theorem for vector payoffs. Pacific Journal of Mathematics. ,vol. 6, pp. 1- 8 ,(1956) , 10.2140/PJM.1956.6.1
D. Ghose, A necessary and sufficient condition for pareto-optimal security strategies in multicriteria matrix games Journal of Optimization Theory and Applications. ,vol. 68, pp. 463- 481 ,(1991) , 10.1007/BF00940065
K. Tamura, S. Miura, Necessary and sufficient conditions for local and global nondominated solutions in decision problems with multi-objectives Journal of Optimization Theory and Applications. ,vol. 28, pp. 501- 523 ,(1979) , 10.1007/BF00932220
A. Charnes, Z.M. Huang, J.J. Rousseau, Q.L. Wei, Cone extremal solutions of multi-payoff games with cross-constrained strategy sets Optimization. ,vol. 21, pp. 51- 69 ,(1988) , 10.1080/02331939008843519
Ichiro Nishizaki, Masatoshi Sakawa, Equilibrium solutions in multiobjective bimatrix games with fuzzy payoffs and fuzzy goals Fuzzy Sets and Systems. ,vol. 111, pp. 99- 116 ,(2000) , 10.1016/S0165-0114(98)00455-2
I. Nishizaki, T. Notsu, Nondominated Equilibrium Solutions of a Multiobjective Two-Person Nonzero-Sum Game and Corresponding Mathematical Programming Problem Journal of Optimization Theory and Applications. ,vol. 135, pp. 217- 239 ,(2007) , 10.1007/S10957-007-9245-6