多目标大博弈中弱Pareto-Berge均衡的存在性

蒲勇健,杨哲

系统科学与数学 ›› 2012, Vol. 32 ›› Issue (1) : 70-78.

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PDF(279 KB)
系统科学与数学 ›› 2012, Vol. 32 ›› Issue (1) : 70-78. DOI: 10.12341/jssms11775
论文

多目标大博弈中弱Pareto-Berge均衡的存在性

    蒲勇健1,杨哲2
作者信息 +

THE EXISTENCE OF WEAKLY PARETO-BERGE EQUILIBRIUM POINTS IN MULTIOBJECTIVE LARGE GAMES

    PU Yongjian1, YANG Zhe2
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摘要

研究了具有任意多个局中人的非合作多目标博弈(多目标大博弈).基于一般非合作博弈中的Berge均衡概念, 定义多目标大博弈中的弱Pareto-Berge均衡.进一步推广了截口定理,得到新的截口定理, 并且利用这个新的截口定理证明多目标大博弈中弱Pareto-Berge均衡的存在性.多目标大博弈中弱Pareto-Nash均衡的存在性结论可作为弱Pareto-Berge均衡存在性的特例给出.

Abstract

This paper considers noncooperative multi-objective games with multi-players (multi-objective large game). According to Berge equilibrium in normal  ames, we introduce the notion of weakly Pareto-Berge equilibrium in multi-objective large games. By generalizing section theorem, we show the existence of weakly Pareto-Berge equilibrium in multi-objective large games. As a special case, we obtain the existence of weakly Pareto–Nash equilibrium points in multi-objective large games.

关键词

多目标大博弈 / 截口定理 / 弱Pareto-Berge均衡 / 弱Pareto-Nash均衡 / 存在性.

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蒲勇健,杨哲. 多目标大博弈中弱Pareto-Berge均衡的存在性. 系统科学与数学, 2012, 32(1): 70-78. https://doi.org/10.12341/jssms11775
PU Yongjian, YANG Zhe. THE EXISTENCE OF WEAKLY PARETO-BERGE EQUILIBRIUM POINTS IN MULTIOBJECTIVE LARGE GAMES. Journal of Systems Science and Mathematical Sciences, 2012, 32(1): 70-78 https://doi.org/10.12341/jssms11775
中图分类号: 91A10         91A40         91A44   
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