The Existence And Generic Stability Of Nash Equilibria

In this thesis, we mainly discuss the existence and generic stability of Nash equilibria for n-person non-cooperative games under weaker conditions.It consists of three chapters.Chapter 1. Preliminaries. We introduce some basic notions and results including completeness, Hausdorff distance, Baire's category and the semi-continuity of set-valued mapping.Chapter 2. Existence of Nash equilibria in H-spaces. Firstly, we obtain an existence theorem of Nash equilibria for n-person non-cooperative games in H-spaces. Then, we get two existence theorems of Nash equilibria with the help of the notions of generalized H-KKM mapping, generalized H -diagonal quasi-concavity and diagonal transfer continuity.Chapter 3. Generic stability of Nash equilibria. Firstly we study the generic stability of Nash equilibria for n-person non-cooperative games and generalized games where strategy spaces are non-convex and payoff functions are non-quasiconcave . Then, we study the generic stability of the solutions of quasi-variational inequality with its application to game theory.