可行策略对应的图像拓扑下广义博弈Nash平衡的稳定性
发布时间：2019-04-20 08:56
【摘要】：以往关于广义博弈Nash平衡的稳定性的研究,均利用可行策略映射之间的一致度量.现考虑在更弱的度量下,利用可行策略映射图像之间的Hausdorff距离定义度量.在此弱图像拓扑下,证明了广义博弈空间的完备性,以及Nash平衡映射的上半连续性和紧性,进而得到广义博弈Nash平衡的通有稳定性.即在Baire分类的意义下,大多数的广义博弈都是本质的.
[Abstract]:In the past, the stability of Nash equilibrium in generalized games was studied by using the uniform metric between feasible strategy maps. In this paper, we consider how to use feasible strategy to map the Hausdorff distance between images to define a metric under weaker metrics. In this weak image topology, the completeness of the generalized game space and the upper semi-continuity and compactness of the Nash equilibrium map are proved. Furthermore, the general stability of the generalized game Nash equilibrium is obtained. That is, in the sense of Baire classification, most generalized games are essential.
【作者单位】： 贵州大学数学与统计学院;贵州财经大学数学与统计学院;
【基金】：国家自然科学基金(No.61472093) 贵州省教育厅自然科学基金(No.黔教合KY字[2015]421) 贵州大学研究生创新基金(No.2016017)
【分类号】：O225
，
本文编号：2461468
[Abstract]:In the past, the stability of Nash equilibrium in generalized games was studied by using the uniform metric between feasible strategy maps. In this paper, we consider how to use feasible strategy to map the Hausdorff distance between images to define a metric under weaker metrics. In this weak image topology, the completeness of the generalized game space and the upper semi-continuity and compactness of the Nash equilibrium map are proved. Furthermore, the general stability of the generalized game Nash equilibrium is obtained. That is, in the sense of Baire classification, most generalized games are essential.
【作者单位】： 贵州大学数学与统计学院;贵州财经大学数学与统计学院;
【基金】：国家自然科学基金(No.61472093) 贵州省教育厅自然科学基金(No.黔教合KY字[2015]421) 贵州大学研究生创新基金(No.2016017)
【分类号】：O225
，
本文编号：2461468
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