Stability Research And Application Of A Class Of Group Games

In this thesis,we mainly study the stability of population games and its application in shared car.Firstly,we study the approximation theorem and generic convergence of population games under the condition of bounded rationality.Then we study the structural stability,robustness and approximation theorem of stable group games under the framework of bounded rationality.Finally,from the perspective of evolutionary game,the model of travelers population game is established,and the relevant factors that affect the choice are analyzed and simulated.The details are given as follows:(1)We mainly study the approximation theorem and generic convergence of population games.Firstly,we prove the approximation theorem of population games under the condition of bounded rationality.Then,by using the method of set-valued analysis,we obtain the result that the solutions of population games have generic convergence under the condition of objective function perturbation.(2)We mainly study a class of special population games.First of all,under the bounded rationality framework,we study the stable population games equilibrium and-equilibrium point sets by constructing rationality function.The research results show that most of stable population games are structurally stable and robust in the sense of Baire category.Then,for stable population games,the problem of whether the approximate solution representing bounded rationality converges to the exact solution representing full rationality is studied,which provides a theoretical support for solving the problem of stable population games.(3)Based on evolutionary game theory,the game relationship among high-end shared cars,low-end shared cars and private cars is established by considering factors such as the quality of shared cars and car-sharing services.The factors affecting travelers’ choice of transportation are analyzed,and the choice behavior and evolutionary path of travelers are simulated with MATLAB software.The research results show that when travelers choose high-end shared car travel,the excess return will increase.Travelers choose low-end shared car travel to obtain less cost and income;When the government increases subsidies for sharing cars and charges for private car parking,travelers will tend to choose high-end shared car travel.