有限理性与KKM点集的稳定性

Bounded Rationality and Stability of KKM's Points Sets

文章首先给出有限理性非线性问题的稳定性结果,然后应用统一结果对KKM点问题构造了问题空间,定义了理性函数,讨论了有限理性下KKM点问题解的稳定性。通过证明其满足统一结论的假设条件,得到了有限理性下KKM点集结构稳定性和鲁棒性结论。并证明了大多数的KKM点问题在Baire分类意义上都是结构稳定的,对ε-平衡也都是鲁棒的,得到了有限理性下KKM点集稳定性的一系列结果。并且,由于在问题研究中考虑了人们只具有有限理性的假设条件,故扩展了KKM点问题结论的应用范围。

It has been studied actively in recent years the consider the bounded rationality in the study of the stability about the solution of nonlinear problems,whose results will fit with the practical situation more easily.In this paper,the unified conclusions of stability for nonlinear problems are given first,and then,with the use of applications of the unified model,problems＇ metric for KKM＇s points problems are constricted and rationality function for KKM＇s points problems are defined,to discuss the stability of solutions for KKM＇s points problems on the bounded rationality.It is proved that KKM＇s points problems are satisfied all of hypothesis conditions of the unified conclusions,we receive the conclusions of structurally stable and robust.Then,it is proved that most of KKM＇s points problems（in the sense of Baire category） are structurally stable and robust to ε-equilibria,finally,the stability results on KKM＇s points problems are given.Moreover,We assume that people only have bounded rationality in the study,so we can enlarge the application scope of the results of the KKM＇s points problems.