在强扰动下广义最大元的稳定性  

Stability of Generalized Maximal Elements under Strong Perturbations

作　　者：周应辉 杨彦龙 

机构地区：[1]贵州大学数学与统计学院,贵州 贵阳

出　　处：《理论数学》2023年第12期3638-3645,共8页Pure Mathematics

摘　　要：本文通过引入由半度量定义的一种更强的扰动,即Hausdorff半度量,代入该扰动后证明广义最大元中强本质集的存在性,进一步得出广义最大元点集稳定性的一些结果。作为应用,该方法也证明了广义最大元策略的Nash均衡的稳定性,对支付函数扰动具有较强的鲁棒性。In this paper, we further derive some results on the stability of generalized maximal elements by introducing a stronger perturbation defined by the semi-metric measure, i.e. the Hausdorff semi-metric measure, and proving the existence of a strong essential set in the generalized maximal element by substituting this perturbation. As an application, the method also proves the stability of the Nash equilibrium of the generalized maximal element strategy, which is robust to payment function perturbations.

关 键 词：稳定性 Hausdorff半度量 广义最大元 

分 类 号：O17[理学—数学]