非线性房价博弈模型动态分析及其控制

Control and Analysis on Nonlinear House Price Game Model

在充分考虑了土地供给、政府、房地产商等诸多因素的基础上建立了非线性市场房价博弈模型,通过研究模型中各重要参数的变化来探讨社会和各方经济收益最大化下的调控方案。研究结果表明:当土地价格调整参数发生变化时,政府与房地产商的总收益和边际收益都有可能进入混沌状态,在模型中通过加入外部控制信号对状态变量的取值进行控制,可以使土地价格和房屋价格经由初始值快速、有效地收敛到纳什均衡点,政府与房产商的总收益也会分别由混沌态进入稳定态, 对控制前后政府的累计收益进行对比发现,控制后政府的累计收益较控制前增长了25．2％。最后给出了与此相应的数值模拟结果。

With the consideration of land supply, government and land agent etc. the nonlinear house price game model was established. Through studying the variation of each important parameter, we analyses the control solution that can maximize social and economic profit. The study result shows that when land price adjustment parameter varies the profit of government and land agent will enter chaotic orbit. Through adding external control signals to the model, land price and house price reach to equilibrium quickly from original point. Meanwhile the profit of government and land agent also converge from chaotic to stable. Finally we use numeral simulation to demonstrate this dynamic behavior. Comparing to precontrol, the profit of government rises 25.5% after being controlled. This research has important actual application value.