具有二期时滞的Bertrand混沌博弈研究

发布时间：2018-10-24 15:42

【摘要】：社会经济的快速发展及各行业的频繁兼并重组使越来越多的市场步入了寡头垄断时代,且市场中各企业的竞争主要体现在价格的竞争,但是目前现存的相关研究大部分是针对双寡头市场引入一期时滞,对于二期及以上的市场研究较少,且研究方法上也存在一定的局限性,因此有必要对二期时滞的双寡头市场的价格竞争进行复杂性分析,以建立相应的价格博弈系统来指导企业发展,其中复杂性分析是目前非线性经济系统的主流研究方法。本文主要完成了以下工作:1.在双寡头价格博弈模型中引入了二期延迟决策,并给出了该模型Nash均衡点的稳定域。通过数值模拟详细分析了市场中采取延迟决策者的数目和延迟参数对稳定域及企业利润的影响,研究发现采取延迟决策的企业数目增加不会对Nash均衡点的稳定域带来影响,但是会带来企业累积平均利润的增加,而延迟参数的增大会扩大系统Nash均衡点稳定域,同时也会降低企业累积平均利润,所以寡头市场中的企业应当采取延迟决策,并适当选取延迟参数。2.为了更加符合实际,模型综合考虑了非对称性产品替代率、有限理性决策等因素。在此基础上,文章对模型进行了复杂性分析,给出了Nash均衡点的稳定域,并通过数值模拟研究了模型中价格调整速度对企业价格、利润、均衡周期等的影响。研究发现,当市场中任一企业的价格调整速度过快都会导致系统陷入混沌状态,并使系统中企业的利润无法实现稳定增长,使企业实现均衡的周期延长。基于此,文章还采用延迟反馈控制法实现了三寡头价格博弈系统混沌状态的控制。3.混沌状态不仅影响企业的价格决策,而且企业利润也会随之产生剧烈波动,变得难以预测。因此,为了抑制和消除混沌状态的影响,本文分别采用延迟反馈控制法和直线控制法对两个模型的混沌状态进行了有效控制,并提出了几项能够帮助企业实施反馈控制的措施:控制产品价格调整速度、降低产品替代率、降低产品边际成本、选择合适的延迟权重系数等,均能够快速帮助系统恢复到企业利润稳步增长的稳定状态。
[Abstract]:The rapid development of social economy and the frequent merger and reorganization of industries make more and more market enter the era of oligarchic monopoly, and the competition of each enterprise in the market is mainly reflected in the competition of price, but at present, most of the related research is to introduce a time lag for the dual oligarch market. Therefore, it is necessary to analyze the complexity of the double oligarchic market of the second-stage time-lag so as to establish the corresponding price game system to guide the development of the enterprise. Complexity analysis is the mainstream research method of nonlinear economic system. This article mainly completes the following work: 1. The second-stage delay decision is introduced in the double oligarchic price game model, and the stable domain of Nash equilibrium point of the model is given. By means of numerical simulation, the influence of the number of decision makers in the market and the delay parameters on the stability domain and the profit of the enterprise is analyzed in detail. The research shows that the increase of the number of enterprises taking the delay decision will not have an impact on the stability domain of Nash equilibrium point. However, there will be an increase in the average profit of the enterprise, while the increase of the delay parameters will expand the system Nash equilibrium point stability domain, and also reduce the accumulated average profit of the enterprise, so the enterprise in the oligarch market should adopt the delay decision and select the delay parameter appropriately. In order to be more realistic, the model comprehensively considers the non-symmetrical product substitution rate, the limited rational decision-making and other factors. On this basis, the complexity analysis of the model is carried out, the stable domain of Nash equilibrium point is given, and the influence of price adjustment speed on the price, profit and equilibrium period of the enterprise is studied by numerical simulation. It has been found that when the price adjustment speed of any enterprise in the market is too fast, it can cause the system to fall into a bad state, and make the profit of the enterprise in the system unable to realize the steady increase, so that the enterprise realizes the balanced cycle extension. Based on this, the paper also adopts the delay feedback control method to realize the three-oligarch price game system control. The state-of-the-art state affects not only the price decision-making of the enterprise, but also the sharp fluctuation of the profit of the enterprise. Therefore, in order to suppress and eliminate the influence of the state of the product, this paper adopts the delay feedback control method and the linear control method to effectively control the state of the price of the two models, and puts forward several measures that can help the enterprise to implement the feedback control: to control the product price adjustment speed, Reducing the product substitution rate, reducing the marginal cost of the product, choosing the appropriate delay weight coefficient, etc. can help the system to restore the steady state of the steady growth of the enterprise's profit.
【学位授予单位】：江西财经大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224.32;F275

【参考文献】