Research On Stability And Algorithm Of Master-slave Game Based On Bounded Rationality

In this paper,we mainly study the stability and algorithm of Nash equilibrium points for single-leader-multi-follower games.Firstly,the existence of Nash equilibrium points is studied for single-leader-multi-follower games under the weak condition.Second,we study the stability of equilibrium point set for single-leader-multi-follower games under the condition of bounded rationality,most of single-leader-multi-follower game are essential in Baire category,that is stability.Then,aiming at the algorithm of Nash equilibrium of single-leader-multi-follower game,and an immune particle swarm algorithm is proposed.This thesis is organized as follows:Chapter 1 is the preface,which mainly outlines the research status of single-leadermulti-follower game at home and abroad.In chapter 2,we mainly introduce the preliminaries,including the single-leadermulti-follower games model,the continuity of set-valued mapping,pseudo continuous,the Berge maximum theorem,the Fan-Glicksberg fixed point theorem and so on.In chapter 3,we mainly study the existence and stability of Nash equilibrium points for single-leader-multi-follower games.The existence of Nash equilibrium point for singleleader-multi-follower games is proved by using the Berge maximum theorem and the FanGlicksberg fixed point theorem under the weak condition.In terms of the stability of equilibrium point,the essential components of the Nash equilibrium point sets of singleleader-multi-follower games are proved from the viewpoint of best response topology.In chapter 4,we mainly study the stability of equilibrium point set for single-leadermulti-follower games under the condition of bounded rationality.First,in locally convex Hausdorff topological space,we introduce the single-leader-multi-follower game model and construct the bounded rationality function.Then,the bounded rationality model M of single-leader-multi-follower games is given.Finally,we study the stability of Nash equilibrium for single-leader-multi-follower games under the essential solution,i.e.,most of single-leader-multi-follower game are essential in Baire category.At the same time,it is pointed out that for the non-essential equilibrium point set,the equilibrium point set obtained by bounded rationality can be used to approximate the equilibrium point set obtained by complete rationality,i.e.,the non-essential equilibrium point set can be approximated by the essential equilibrium point set.In chapter 5,we mainly present an immune particle swarm algorithm for leaderfollowers game on solving the Nash equilibrium problem.The antibody concentration inhibition mechanism and immune memory function of immune algorithm is involved into the original swarm algorithm.The proposed algorithm has not only the properties of the original swarm algorithm,but also improves the abilities of seeking the global optimization result.The computer simulation results demonstrate that the proposed algorithm is effective.