The Construction Of Pricing Model For The House Based On The Differential Game

With the housing system reforming, housing commercialization and paid use of land, real estate industry rapidly develops and expanses in China. The house price is the economic leverage to adjust the profits of real estate industry and it is advantageous to promote the development of real estate. However, the rapid development of real estate industry in recent years has also sparked a series of problems; one of the most prominent is the high housing prices, which transforms it from the people’s livelihood industry for profiteering industry. High housing prices is not only a distortion of the real estate market itself, but also will affect the sustainable development of our country, social stability and national economic security. The US financial crisis is caused by the housing bubble, so it can be seen that the real estate industry to the economy as a whole plays a vital role. Determine the correct pricing model, therefore, is of great significance for developers to stand in a strong position in the competition, and for promoting the healthy development of China’s real estate industry. At present, a lot of pricing models are static pricing methods, namely not changing house prices in the short term, but it is hard to adapt to today’s rapidly changing real estate market.In this paper, price differential equation of state is introduced, at the same time, time variable is considered, and master-slave differential game model is established by determining the government and the decision variables of the real estate and payoff function. Besides, it intends to solve the model by constructing the HJB equation using backward induction method. After the acquisition of government optimal decision n and the optimal decision of q value, the real estate value p is determined. Through numerical simulation and image, it can be seen that house prices will decline, and the government decision-making variable compensation payment (tax) amount of decision variables for the housing and real estate developers will become rising trend.