Of Ky Fan Inequalities Stability In Game Theory

It is well-known that solutions of some nonlinear problems or equilibrium problems are not unique,and some times even infinite,and also some of them may be unreasonable,so many scholars pay much attention to the refinements of solutions.In this paper,we introduce a new method to eliminate those undesirable solutions of Ky Fan inequality which plays an important role in nonlinear analysis,and consider the applications to n-person general noncooperative game.It consists of two chapters.In chapter 1 we mainly consider the refinement of Ky Fan's points.The main idea of refining is to perturb the domain set X×X,by taking a sequence of sets in the interior of X×X converging to X×X,and then find a sequence of approximate Ky Fan's points that are convergent in the sequence of sets.If the convergent approximate Ky Fan's points converge to a Ky Fan's point of function f on X×X,we call that this Ky Fan's point is stable under the perturbation.At last,we show the existence of the stable Ky Fan's point.In chapter 2 we study the refinements of Nash equilibrium of n-person general noncooperative game by perturbing the persons' strategy sets using the outcome of the chapter one.