| 不确定性下强Berge均衡的存在性 |
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| 引用本文： | 邓喜才,向淑文,左羽.不确定性下强Berge均衡的存在性[J].运筹学学报,2013,17(3):101-107. |
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| 作者姓名： | 邓喜才 向淑文 左羽 |
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| 作者单位： | 1. 贵州大学数学系，贵阳 550025
2. 贵州师范学院数学与计算机系，贵阳 550018 |
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| 基金项目： | 国家自然基金 (No. 11161008), 教育部博士点基金 (No. 20115201110002), 贵州省科学技术基金 (Nos. [2012]2289, [2013]2235) |
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| 摘 要： | 在已知不确定参数变化的范围下，研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性，基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念，给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义，并利用Fan-Glicksberg不动点定理证明其存在性，最后用算例验证其可行性.
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| 关 键 词： | 非合作博弈 广义非合作博弈 不确定性 强Berge均衡 存在性 |
Existence of strong Berge equilibrium under uncertainty |
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| DENG Xicai,XIANG Shuwen,ZUO Yu.Existence of strong Berge equilibrium under uncertainty[J].OR Transactions,2013,17(3):101-107. |
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| Authors: | DENG Xicai XIANG Shuwen ZUO Yu |
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| Institution: | 1. Department of Mathematics, Guizhou University, Gui Yang 550025, China
2. Department of Mathematics and Computer, GuiZhou Normal College, GuiYang 550018, China |
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| Abstract: | Under the assumption that the domain of the undetermined parameters is known, the existence of strong Berge equilibrium for non-cooperative games and generalized non-cooperative games are investigated. Based on the concept of strong Berge equilibrium and NS-equilibrium for non-cooperative games under uncertainty, the notions of strong Berge equilibrium for non-cooperative games and generalized non-cooperative games under uncertainty are defined. Further, the existence of the equilibrium for non-cooperative games and generalized non-cooperative games are proved by using Fan-Glicksberg fixed point theorem. Finally, a numeric example illustrates the feasibility of the proposed method. |
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| Keywords: | non-cooperative games generalized non-cooperative games uncertainty strong Berge equilibrium existence |
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