| 图象拓扑下的Ky Fan引理解集的本质连通区及其在对策论上的应用 |
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| 引用本文： | 周永辉,向淑文. 图象拓扑下的Ky Fan引理解集的本质连通区及其在对策论上的应用[J]. 应用数学学报, 2005, 28(2): 281-287 |
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| 作者姓名： | 周永辉 向淑文 |
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| 作者单位： | 1. 浙江大学数学系,杭州,310027
2. 贵州大学数学系,贵阳,550025 |
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| 基金项目： | 贵州省自然科学基金，贵州省优秀人才省长专项基金 |
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| 摘 要： | 本文在集值映射的图象拓扑意义下,证明了赋范线性空间中的Ky Fan引理的解集的本质连通区的存在性,由此得到一类对策的Nash平衡点集的本质连通区的存在性.
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| 关 键 词： | 图象拓扑 Ky Fan引理的解 Nash平衡 本质连通区 |
THE EXISTENCE OF ESSENTIAL COMPONENTS OF THE SET OF SOLUTIONS OF KY FAN''''S LEMMA AND ITS APPLICATIONS TO GAME THEORY |
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| ZHOU YONGHUI,XIANG SHUWEN. THE EXISTENCE OF ESSENTIAL COMPONENTS OF THE SET OF SOLUTIONS OF KY FAN''''S LEMMA AND ITS APPLICATIONS TO GAME THEORY[J]. Acta Mathematicae Applicatae Sinica, 2005, 28(2): 281-287 |
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| Authors: | ZHOU YONGHUI XIANG SHUWEN |
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| Abstract: | We prove that for all problems of Ky Fan's Lemma in normed vector space there exists at least one essential component of the set of solutions of Ky Fan's Lemma. As a consequence, we deduce that for any general n-person game with some convexity and continuity conditions, there exists at least one essential component of the set of Nash equilibrium points. |
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| Keywords: | graph topology Nash equilibrium Ky Fan's Lemma essential component |
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