The Image Topology Of Set-valued Mapping And The Stability Of Nash Equilibrium Point Of Generalized Game

In this thesis,we mainly study the stability of generalized games’ Nash equilibria under the graph topology of feasible strategy correspondence.Firstly,we study the existence of generalized games’ Nash equilibria.Secondly,we present a weaker metric in this thesis and uses Hausdorff distance of graph of feasible strategy correspondence to study the generic stability of Nash equilibria and bounded rationality and the stability of generalized games’ Nash equilibria.Finally,we study the well-posedness of generalized games.This thesis is organized as follows:Chapter 1,we introduce the research history of Nash equilibria’ refinement and stability,the development history and research status of generalized games,and the weak graph topology of set-valued mappings.Chapter 2,we introduce several basic definitions and preliminaries,such as compactness of topological space and convexity of linear space,the continuity of set-valued mappings and it’s related properties,Brouwer fixed point theorem and Kakutani fixed point theorem and so on.Chapter 3,for the generalized games which satisfy particular conditions,we prove the existence of generalized games’ Nash equilibria by using Fan-Glicksberg fixed point theorem.Chapter 4,this thesis presents a weaker metric and uses Hausdorff distance of graph of feasible strategy correspondence,then proves the generic stability of generalized games’ Nash equilibria under the uniform disturbance of payoff functions and graph disturbance of feasible strategy correspondences.Chapter 5,under the framework of bounded rationality model,we also prove the completeness of parameter space.Then the behavior mapping and rational function are defined.Consequently,the result for the stability of generalized games’ Nash equilibria under bounded rationality is obtained.Besides,we also obtain bounded rationality and fixed point problems’ stability concerning upper semi-continuous set-valued mappings.Chapter 6,based on the defined behavior mapping and rational function,we prove the well-posedness of generalized games and the well-posedness of fixed point problems,respectively.