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Evolutionary Game Research on the problem of Rural College Graduates returning home for Development in China

Abstract: Under the background of Rural Revitalization Strategy in the new era, in order to add new impetus,bring new opportunities and create newsituation for the increasingly hollow countryside, the country actively calls on rural university graduates toreturn home to start a business and obtain employment. Despite the active implementation of national policies, the enthusiasm of college graduates to return home is not as strong as expected, so promoting the activity of rural college graduates and encouraging local governments to build a good environment for entrepreneurship and employment are the problems we are facing. Based on the evolutionary game theory, this paper establishes the evolutionary game model of decision-making behavior between local government and rural college graduates, and analyzes evolution processes and results of the whole game system in the different restriction on parameters. The most ideal strategic state is that local governments forwardly support graduates and college graduates actively return to their hometown for entrepreneurship and employment, which can meet the needs of economic development and benefit both sides, according to the evolution of this state, some reasonable suggestions are put forward from different levels.


Model construction:
The two groups of the game are local government and college graduates. According to the actual situation, under the condition of both sides' limited rationality, the local government's strategy is to support (create a good environment for entrepreneurship and employment), not to support; the college graduates' strategy is to return home, not to return home. The specific parameters are assumed as follows: F refers to the income obtained by the local government in organizing the normal agricultural production activities when the university graduates do not return home.
T 1 refers to the gain brought to the local economy when the university graduates return home for employment with the support of the local government.   Among the group of university graduates, x percent of them choose the return strategy, others choose not to returnstrategy.
Among the group of local government group, y percent of them choose the support strategy,others choose not to support strategy.
Based on the above assumptions, the game income matrix of both parties is obtained as follows:

Model analysis:
1 U is the expected revenue of college graduates when choosing "returning home" strategy. 2 U is the expected revenue of college graduates when choosing "returning home" strategy. U is the average expected revenue of college graduates.
V is the expected revenue of local governments when choosing "support" strategy. 2 V is the expected revenue of local governments when choosing "not support" strategy. V is is the average expected revenue of local governments.
From the above calculation and analysis, we can establish the replication dynamic equation as follows: The Jacobian matrix J of the system : The trace of Jacobian matrix J :

Analysis of equilibrium and stability strategy:
Let f (x) = 0, g (y) = 0. By solving the duplicate dynamic equations, we can get the equilibrium points of the above game system under different constraints. According to Jacobian matrix stability theorem, we analyze the evolution path and equilibrium stability strategy of the whole system in each case. There are nine cases in total, as shown in the following table.  follows: on the one hand, the financial support provided by the central government is limited, which can not attract college graduates to go back to their hometown actively for entrepreneurship and employment. On the other hand, the cost of local government to create a good environment for college students returning their hometown is high, so that they are not willing to invest in it. In addition, a broader development platform for college graduates in economically developed cities is also one of the factors that they choose not to return hometown for entrepreneurship and employment.
In the seventh case, it can be seen from the given phase diagram that the system will converge to (1,0) , that is, university graduates choose the strategy of returning to their hometown for entrepreneurship and employment, but local governments choose the strategy of not supporting. This is a suboptimal solution of the whole evolutionary system. In this situation, although the local government don't give certain support, university graduates still return home to start their own business and employment, to a certain extent, which promotes the development of rural undertakings. But lack of local government coordination makes the rich resources in rural areas not be fully developed and utilized, and college students need to face many difficulties under the existing rural conditions, they are not motivated to devote themselves to the rural cause.
In the eighth case, it can be seen from the given phase diagram that the system will converge to (0,1) , that is, university graduates choose the strategy of not returning to their hometown for entrepreneurship and employment, but local governments choose the strategy of supporting. In this evolution process, although the central government provides financial support to the local government which creates a good employment environment, the graduates don't actively return to their hometown to start their own businesses, which undoubtedly results in a waste of resources. The state invest in the policy, but will suffer losses.
In the ninth case, the system has five equilibrium points, (1,1) is the evolutionary stable point among them, S(x*,y*) is the saddle point, it can be seen from the given phase diagram that the system will converge to (0, 0) when the initial state is in the lower left area B , that is, college graduates choose not to return to their hometown for entrepreneurship and employment, and local governments choose not to support the strategy; correspondingly, the system will collect (1,1) when the initial state is in the upper right area A, that is, college graduates choose the strategy of returning to their hometown for entrepreneurship and employment, and local governments choose the strategy of support, which is a kind of benign game state we hope to achieve. So we know that the evolution process of the whole system depends on the initial state of the system and the position of the saddle point. In order to achieve the desired state, we can expand the area A in the upper right through the change of parameters, so that the system can evolve to benign state as much as possible. The changes of specific parameter to expand area A are as follows: which not only has the opportunity to reduce the operational cost paid by the local government, but also can fully meet the needs of college graduates, so that they can actively return to their hometown for entrepreneurship and employment. Meanwhile, local governments also need to solve the difficulties they face in rural undertakings, and provide precise help.
c. The process of training students in colleges is targeted. For the rural graduates who are willing to return home, colleges should offer some courses on rural development, entrepreneurship and employment, so that they can learn and master the relevant knowledge in advance, and improve their practical ability. This will not only be conducive to the return of graduates to less wall, more benefits, but also help local governments to trust the ability of university graduates and actively guide them to a better direction.