房地产市场非线性博弈模型及其内在复杂性研究
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摘要
在国民经济连续多年保持高速增长的发展态势下,我国房地产市场进入到大规模的市场化开发阶段,经济的增长、城市化进程的加快以及人们对改善性住房需求的不断增加,促使我国大部分城市的房价增长迅速。随着国家宏观调控的逐渐深入,转型期的房地产业呈现出增长波动的特点,并开始朝着宏观调控预期的方向发展。由于房地产关系到我国经济的健康发展、土地资源的合理配置、房产的有效开发以及消费者合法权益的保护,而且在房地产开发过程中涉及到各级政府、房地产开发商和广大消费者的利益,所以如何有效的把握和协调各利益主体之间的关系便成为一个十分具有现实意义的课题。
在此背景下,本文以国内外相关领域的研究成果为基础,运用动态经济学理论和非线性动力学方法,深入的分析了我国房地产市场三大利益主体间的博弈关系,以期为此类问题的研究提供方法和思路。本文主要完成了以下工作:
1、根据非线性蛛网理论建立了较为符合中国国情的具有二维离散特性的房地产动态博弈模型。以地价对房价的影响为切入点,揭示了政府与房地产开发商之间的博弈关系。研究发现随着参数的变化,系统的纳什均衡解将发生分岔从而失去稳定性,并最终出现混沌行为。在此基础上运用K.Pyragas所提出的延迟反馈控制方法对模型的混沌状态进行了有效的控制并讨论了控制后系统的稳定性。
2、应用博弈论和预期理论,研究了房地产商与购房消费者之间关于市场房价预期的动态博弈关系。建立了关于预期房价模型,引入调整参数模拟房地产商对商品房供给进行控制的动态过程。采用数值模拟的方法演示了博弈主体之间的内在复杂行为。
3、分析了房地产开发商之间的动态关系。应用Bertrand和Stackelberg模型对生地、熟地和商品房的定价策略进行了研究。分别讨论了开发商合作博弈与非合作博弈时系统的均衡解,对合作与非合作定价策略的效率进行了比较。综合考虑了如何提高政府收益以及降低市场房价的问题。
4、在充分研究了博弈主体两两间的关系基础上,以政府、房地产商和消费者三方关于市场房价的博弈过程为背景,建立了一个三维离散非线性动力学模型。研究表明该系统可通过倍周期分岔和环面失稳等方式进入混沌状态。在此模型中,政府对土地价格的调整以及房地产商对房价的调整在博弈动态地趋于Nash均衡过程中起着非常重要的作用。
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.
在此背景下,本文以国内外相关领域的研究成果为基础,运用动态经济学理论和非线性动力学方法,深入的分析了我国房地产市场三大利益主体间的博弈关系,以期为此类问题的研究提供方法和思路。本文主要完成了以下工作:
1、根据非线性蛛网理论建立了较为符合中国国情的具有二维离散特性的房地产动态博弈模型。以地价对房价的影响为切入点,揭示了政府与房地产开发商之间的博弈关系。研究发现随着参数的变化,系统的纳什均衡解将发生分岔从而失去稳定性,并最终出现混沌行为。在此基础上运用K.Pyragas所提出的延迟反馈控制方法对模型的混沌状态进行了有效的控制并讨论了控制后系统的稳定性。
2、应用博弈论和预期理论,研究了房地产商与购房消费者之间关于市场房价预期的动态博弈关系。建立了关于预期房价模型,引入调整参数模拟房地产商对商品房供给进行控制的动态过程。采用数值模拟的方法演示了博弈主体之间的内在复杂行为。
3、分析了房地产开发商之间的动态关系。应用Bertrand和Stackelberg模型对生地、熟地和商品房的定价策略进行了研究。分别讨论了开发商合作博弈与非合作博弈时系统的均衡解,对合作与非合作定价策略的效率进行了比较。综合考虑了如何提高政府收益以及降低市场房价的问题。
4、在充分研究了博弈主体两两间的关系基础上,以政府、房地产商和消费者三方关于市场房价的博弈过程为背景,建立了一个三维离散非线性动力学模型。研究表明该系统可通过倍周期分岔和环面失稳等方式进入混沌状态。在此模型中,政府对土地价格的调整以及房地产商对房价的调整在博弈动态地趋于Nash均衡过程中起着非常重要的作用。
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.
引文
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