The Existence And Stability Of Weak Nash Equilibria For Population Games

In the thesis,we introduce costs into the classical population games.In such games,the cost is corresponding to each pure strategy.We focus on the the existence and stability of Nash equilibria in those games and its application in “ease the burden of excessive homework and off-campus tutoring for students undergoing compulsory education”policy.Firstly,the cost function is introduced into the population games and the population games with uncertain parameters respectively.Then the existences and stabilities of their equilibria are researched.Secondly,the impact of costs on the behavior of three-party strategies under the “ease the burden of excessive homework and off-campus tutoring for students undergoing compulsory education”policy is studied by simulation analysis under evolutionary games.There are six chapters in this thesis,as follows:Chapter 1 mainly introduces the research background,significance and status of population games,population games with uncertain parameters and evolutionary games.Chapter 2 mainly presents the population games model,population games with uncertain parameters,bounded rationality model and replication dynamics.The 3rd chapter mainly studies the existence and generic stability of weak Nash equilibria in population games.Firstly,population games with costs is established and a weak Nash equilibrium is proposed by introducing the costs function.The effects of costs on Nash equilibria is also illustrated by an example.In addition,the existence of weak Nash equilibria is proved by Brouwer fixed point theorem.Finally,the generic stability of weak Nash equilibria for population games is proved by Fort theorem when the net profit function is perturbed.Chapter 4 deals with the stability of weak NS equilibria for population games with uncertain parameters under bounded rationality.Firstly,the costs function is introduced into population games with uncertain parameters,a weak NS equilibrium is proposed,and the effects of costs on NS equilibria is also verified by an example.Furthermore,the existence of weak NS equilibria is proved by Kakutani fixed point theorem.Finally,by establishing a rational function,it is proved that a bounded rationlity model is structurally stable and robust for -weak NS equilibria when the net profit function is perturbed.Therefore,in the sense of Baire category,weak NS equilibria for population games with uncertain parameters is generic stability under the framework of bounded rationality,and the correctness of the result is verified by a example.Chapter 5 contributes to evolutionary games analysis and simulation for “ease the burden of excessive homework and off-campus tutoring for students undergoing compulsory education”policy.Firstly,the model of replicative dynamics among the population of students,the population of education and training institutions,and the departments of education regulation is established.The result shows that(1)for supervisory departments,when the costs of negative regulation by the supervisory departments are greater than the corresponding increase profits,the supervisory departments prefer to choose “active regulation”strategy.(2)Simultaneously,for education and training institutions,they are actively regulated by supervisory departments and the costs of irregular operations of education and training institutions are greater than the corresponding additional benefits,education and training institutions prefer to choose “lawful operation”strategy.(3)For students,when the supervisory departments actively regulate the education and training institutions that lawfully operate,and the costs of purchasing courses are greater than the additional payoffs from purchasing courses,students are better to choose “don’t buy courses”strategy.In this case,the pressure and burden for students can be truly reduced,the chaos in education and training can be rectified,thus finally the goal of this policy can be realized.Chapter 6 makes a brief summary and prospect for the thesis.