非自映射不动点集的稳定性及其在博弈中的应用

On the stability of fixed-point set for non-self mapping and application in game theory

运用一致拓扑方法研究了函数扰动条件下非自映射不动点集的本质稳定性及其在博弈论中的应用。结果表明,大部分非自映射的不动点集都是本质稳定的,在不动点集中至少存在一个极小本质集并且每一个极小本质集都是连通的,进一步证明了不动点的本质稳定连通区的存在性,推广了相应文献的结果;作为不动点的本质稳定性和连通性结果的应用,利用不动点与非合作博弈的Nash平衡点集之间的联系,导出了Nash平衡点集的本质稳定连通区的存在性定理。

This article studies the essential stability of fixed-point set for non-self mapping under the condition of function perturbation using uniform topology and its application in game theory.The results show that most of the fixed-point sets of non-self mappings are essentially stable and there exists at least one minimal essential set,and each minimal essential set is connected.Furthermore,this proves the existence of essential components of fixed-points.These generalize some corresponding results in references.As the part of the application about the essential stability and connectivity of fixed-points,the existence of essential connected components of the set of Nash equilibrium point for non-cooperative game is derived by the connection of fixed points and Nash equilibrium points for non-cooperative game.