有限理性与图像拓扑下Ky Fan截口定理问题的稳定性

Bounded rationality and stability of the problems of Ky Fan's section theory in the sense of graph topology

利用集值映射图像之间的Hausdorff距离定义度量,在图像拓扑意义下,建立Ky Fan截口定理问题的有限理性模型.借助于非线性问题的有限理性模型统一研究稳定性的方法,证明大多数的Ky Fan截口定理问题在Baire分类意义下都是结构稳定的,对ε-近似解集也是鲁棒的,从而可以用有限理性条件下得到的ε-近似解集来逼近完全理性条件下得到的解集.

In this paper, a metric is defined by using the Hausdorff distance of graphs of se--valuemappings, and bounded rational model for the problems of Ky Fants section theory is established in thesense of graph topology. By virtue of the unfied stability method of bounded rational model for nonlinearproblems, it is proved that themost of the problems of Ky Fan’s section theory （in structurally stable and robust to the set of ε- approximate solutions, thus the set of ε- approximate solutions obtained under bounded rationality can be approximated by the set of conditions.