| 弱伪连续向量值函数及其在多目标博弈中的应用 |
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| 引用本文： | 张广,邬冬华,高静.弱伪连续向量值函数及其在多目标博弈中的应用[J].运筹学学报,2015,19(1):92-98. |
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| 作者姓名： | 张广 邬冬华 高静 |
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| 作者单位： | 1. 上海大学管理学院, 上海 200444; 2. 上海大学数学系, 上海 200444; 3. 马陆育才联合中学, 上海 201801 |
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| 基金项目： | 上海自然科学基金(No. 09ZR1411100), 上海市重点学科基金(No. S30104) |
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| 摘 要： | 基于对弱伪连续实值函数的研究, 提出向量值函数关于锥的弱伪连续定义, 并建立了向量值函数$R_+^k$弱伪连续与实值函数弱伪连续的对应关系. 作为弱伪连续向量值函数的应用, 给出了弱伪连续下的向量值Ky Fan点的存在性定理, 并通过该定理证明了伪连续向量值支付下的多目标博弈弱Pareto-Nash平衡点的存在性定理.
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| 关 键 词： | 弱伪连续 向量值函数 向量值函数Ky Fan点 多目标博弈 |
| 收稿时间： | 2013-12-19 |
The weakly pseudocontinuous of vector-valued functions and the application in multi-objective games |
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| ZHANG Guang,WU Donghua,GAO Jing.The weakly pseudocontinuous of vector-valued functions and the application in multi-objective games[J].OR Transactions,2015,19(1):92-98. |
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| Authors: | ZHANG Guang WU Donghua GAO Jing |
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| Institution: | 1. School of Management, Shanghai University, Shanghai 200444, China; 2. Department of Mathematics, Shanghai University, Shanghai 200444, China; 3. Malu Yucai Joint Middle School, Shanghai 201801, China |
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| Abstract: | In this paper, based on the study of pseudocontinuous real-valued functions, a definition of the weakly pseudocontinuous of vector-valued functions on cone is proposed. And a weakly pseudocontinuous relationship is established between the vector-valued functions on $R_+^k$ and the real-valued functions. As an application of the weakly pseudocontinuous of vector-valued functions on cone, the existence theorem of weakly Pareto-Nash equilibrium in multi-objective games with the pseudocontinuous payoffs is proved by the improved vector-valued Ky Fan points. |
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| Keywords: | weakly pseudocontinuous vector-valued functions vector-valued Ky Fan points multi-objective games |
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