Bounded Rationality and Stability of KKM's Points Sets
Zhang De-jin · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2011
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 e-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.