利他扰动与Nash均衡点集的利他稳定性

Altruistic Perturbation and Altruistic Stability of the Set of Nash Equilibrium Points

引入了一个新的利他扰动.定义了KyFan点集的利他本质集,进一步证明在此扰动下,Ky-Fan点集的利他本质连通区的存在性.证明了满足一定条件的n人非合作博弈中,Nash均衡点集至少存在一个利他本质连通区,而且Nash均衡点集的每一个本质集必是利他稳定集,Nash均衡点集的本质连通区也是利他本质集连通区.

By introducing a new perturbation, called altruistic perturbation,and a concept of altruistic essential sets of KyFan＇s points, the existence of altruistic essential component in the perturbation was established. The application shows that for any n-person noncooperative games under some condition, there exists at least one altruistic essential component of the set of Nash equilibria. Each essential set are altruistic stable set, and the essential component of the set of Nash equilibrium points are also altruistic essential component.