Nonlinear Game Model And Its Inherent Complexity In Real Estate Market

As the national economy maintained a high growth momentum of development in consecutive years, China's real estate market has entered a marketizational development period. Housing prices in most cities rise rapidly due to the economic growth, the accelerated process of urbanization and increase in the demand of ameliorative housing from consumers. Thanks to gradually deepening of the macro regulation and control, the real estate industry in a transition period shows a characteristic of fluctuations in growth and starts toward the expected direction of macro-control. The real estate especially concerns the economic development, the rational disposition of land resources and the improvement of people's living standard.In the operational course of various procedures from land purchase , housing project development and construction to housing consumption and service,it involves the interests of all parties' concern including the government,real estate developer,vast majority of consumers and so on.So how to comprehend and harmonize the relation among each agent is a practical task. It has an important meaning to analyze the game relation based on the behaviors of main participants in the land purchase market and house consuming market with the use of nonlinear economic theory. The main content of this dissertation is as follows:First, a nonlinear real estate model is established by means of cobweb theory, where the demand function and supply function are quadratic. The thesis investigates the game relation between government and real estate developers through analysis the influence of land price on housing price. It finds that as some parameters varied, the stability of Nash equilibrium is lost through period doubling bifurcation. The chaotic features are justified numerically. The delayed feedback control method proposed by K.Pyragas is applied to control the chaos of system, and the system stability is also discussed.Second, on the basis of game theory and expectations hypothesis this work analyzed the dynamic ration between real estate and consumers. The expected housing prices game model is established. Through introducing regulative parameters into the model the players'game behavior is demonstrated. Numerical simulations show the dynamic game behavior. Third, the relation between real estate developers is analyzed. Then the price decision of land and housing is studied by using Bertrand and Stackelberg models. The equilibrium solutions about cooperative game and non-cooperative game are also discussed. Efficiencies of each price decision are further compared after government profit as well as housing prices are taken into consideration.Fourth, after sufficient investigating the relation between each agent, a discrete nonlinear model of real estate is derived. Based on which the complex relation and its evolutionary trend among government, consumers and real estate developers is described. It finds that system chaos can be obtained through quasi-periodic transition and double-periodic bifurcation. In this model, government plays an important role on adjust land price to gain Nash equilibrium, also real estate developers'adjustment on housing price can't be ignored.