【摘要】：以往關于廣義博弈Nash平衡的穩(wěn)定性的研究,均利用可行策略映射之間的一致度量.現考慮在更弱的度量下,利用可行策略映射圖像之間的Hausdorff距離定義度量.在此弱圖像拓撲下,證明了廣義博弈空間的完備性,以及Nash平衡映射的上半連續(xù)性和緊性,進而得到廣義博弈Nash平衡的通有穩(wěn)定性.即在Baire分類的意義下,大多數的廣義博弈都是本質的.
[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.
【作者單位】： 貴州大學數學與統(tǒng)計學院;貴州財經大學數學與統(tǒng)計學院;
【基金】：國家自然科學基金(No.61472093) 貴州省教育廳自然科學基金(No.黔教合KY字[2015]421) 貴州大學研究生創(chuàng)新基金(No.2016017)
【分類號】：O225
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本文編號：2461468