Fixed Point Set Of Stability And Its Applications In Game Theory

This thesis research the stability of fixed points and applications in noncooperative game theory,which is organized as follows.It is mainly divided into two sections:In Chapter 1 we review some classical results in fixed point theory and give some preliminaries.Then we introduce the notion of essential components and strongly essential components of fixed points under perturbations of the maps and/or domains.We obtain some existence of essential components of fixed points.In Chapter 2,we present some applications of the stability of fixed points in noncooperative game theory.Specifically,we introduce the notion of essential components and strongly essential components of Nash equilibria under perturbations of payoff functions and/or strategy spaces and get some existence results.