Nash Equilibrium Refining And The Stability Of Related Problem Solutions Are Based On Bounded Rationality

In this thesis,we mainly study the stability of equilibrium points with bounded rationality.Firstly,by studying the stability o fε-Ky Fan points and then to study the stability of ε-equilibrium points of n-person non-cooperative game.Secondly,the stability of the bounded rationality equilibrium point set is studied for generalized games in the framework of the bounded rationality model including the perturbation of rationality function,and studying the relationship between the essential equilibrium point set of bounded rationality and the(λ,φ,ε)stability of the model M.Finally,the bounded rationality model is generalized,after generalization,the bounded rationality model can characterize incomplete rationality caused by various deviations.The whole text is divided into five chapters,as follows:The first chapter:preface,which mainly introduces the research results of Nash equilibrium refinement,and about the research background on bounded rationality,and the current research status at home and abroad.The second chapter:general non-cooperative game model,upper and lower semi-continuity of set-valued mappings,Fort lemma,Hausdorff distance and so on.The third chapter:we mainly study the stability of ε-equilibrium.The existence of ε-Ky Fan points and n-person non-cooperative game ε-equilibrium points is proved under the condition that X is a non-empty convex compact set in Hausdorff linear topological space E.In terms of stability of the equilibrium point set,the concept of the essential component of the solution set of the nonlinear problem is introduced,and it is proved that for any number pair(φ,ε)that satisfie conditions,the ε-Ky Fan point set has an essential component.As an application,the set ofε-equilibrium point has at least one essential component for an n-person non-cooperative gameThe fourth chapter:we mainly study the stability of bounded rational solutions This part of the content is based on the original results,further considering the perturbation of the rationality function.First,we build an abstract model M,and we define stability and robustness different from literature[1].Under the assumptions,the model M is(λ,φ,ε)stable and(λ,φ,ε)robust to most(λ,φ,ε)∈Λ×Φ×R+.Finally,we construct a rationality function space for generalized games and give its bounded rationality model and verify its hypothetical conditions,and finally we conclude that most of the bounded rationality equilibrium point sets are stable in the sense of Baire category.The fifth chapter:we generalize the bounded rationality model,which bounded rationality solution is no longer limited to the bias of the people’s judgment to the solution,by introducing mutation and the scope of the variation,the bounded rationality model can consider deviations caused by various factors.As a special model,there are deviations in the judgment of the players on the payoff and the strategy set.