Study On Two Types Of Stackelberg Differential Game In Chinese Real Estate Market

In economics, Stackelberg differential game is often used to explain the players'dynamic rational behaviors. Government, as the behavior subject participated in the game, is regarded as the leader by common practice in academia, while the other subjects are considered as followers. On this basis, by constructing and solving the differential game model of unequal status, this mathematical tool is not only used to explain economic phenomena, but also to provide policy suggestions for government departments.The real estate market has been focused all along by domestic academia for several years, and most of the existing literature always emphasizes on analyzing its empirical results and discussing relevant policy suggestions. Although game theory for studying real estate market is also an effectual tool, the literatures are still relatively rare for discussing this market by comprising game model and cybernetics. The major work of this dissertation is to construct and discuss the two types of Stackelberg differential game led by government by introducing differential game theory into the study of game relationship in real estate market.In the first model, regarded the differential game between local government and real estate enterprise as the basic unit, inter-governmental non-cooperative game model and cooperative game model are built under special constraints. Government games with enterprises by utilizing land supply and interest rate policy. And by introducing Bang-Coast-Bang control, the payoffs of the local governments in two models are compared under unconventional proof method. In the second model, the number of players was reduced to two, the differential game model between local government and real estate speculators is built, and local government games with speculators by utilizing the property tax policy. By introducing Bang-Coast-Bang control and being with a more in-depth study, the trend of players'rational behaviors are emphatically analyzed, and the study provide government departments corresponding policy suggestions.The main conclusions are:â‘ In terms of real estate enterprises: Favorable real estate enterprises tend to hoard land, ordinary ones are more likely to speed up the land development. Intensified competitions among real estate enterprises would make their behaviors be inclined to two extremes, complete land-hoarding and complete land-developed. However, if the intensified competitions would bring extra welfare to residents is not clear.â‘¡If the central government had possibility to unify plan of the local governments'land-supplying, Pareto improvements for each local government's objective would be achieved effectively. Moreover, it's necessary to consider overall situation in setting benchmark interest rate. The better way is to gather local information, rather than to weigh each local government's interest rate admonition.â‘¢Local government always needs concern about real estate speculators'behaviors all along to set the dynamic property tax rate, and act synchronized with speculators'actions as far as possible. Dynamic property tax rate adjustment should follow: improper too long interval, each time slight variation, consistent varying tendency. In addition, once property tax is applied, it won't be abolished. It is appropriate for government to maintain a dynamic rate to just inhibit house-hoarding. Furthermore, in order to avoid property tax transferred and general rising of house price in mid-term or long-term, high rate should be adopted at the very beginning of property tax reformation.â‘£Bang-Coast-Bang control is caused by Stackelberg differential game combining Bang-Bang control(Generally speaking, the Coast control here satisfies singular arc.). If two players'objectives are both explicitly shown as Bang-Bang control in a Stackelberg differential game system, the followers will chose Bang-Coast-Bang control (The Coast control here satisfies singular arc.), and the leader will chose Bang-Coast-Coast control (The first Coast control period is not on a singular arc, the second one is a Bang-Bang control with time-varying boundary.). And the reason for this kind of control cases is that, the leader have an explicit co-state constraint and an implicit coupled constraint.