含时滞的Bertrand价格博弈模型动态分析及混沌控制研究
发布时间:2018-03-04 21:27
本文选题:Bertrand模型 切入点:价格博弈 出处:《江西财经大学》2016年硕士论文 论文类型:学位论文
【摘要】:近年来,随着互联网以及电子商务的广泛应用和推广,消费者可以足不出户掌握同类产品的所有价格信息,因此,在保证产品质量的前提下,价格优势在市场竞争中体现得愈发明显。以往关于市场中寡头垄断竞争的研究,多是围绕产量博弈进行的,涉及价格博弈的研究较少。因此,本文在Bertrand模型、系统稳定性理论以及混沌理论的基础上,研究了寡头垄断市场竞争中企业之间进行价格博弈的动力学特性及其混沌控制,分析了企业价格决策会受到哪些因素的影响,以及面对这些因素所产生的消极作用,应采取何种有效措施加以抑制和消除。本文主要完成了以下三个方面的工作。(1)本文在Bertrand价格博弈模型的基础上,引入产品差异来避免产生"Bertrand悖论"现象,并且考虑企业定价决策过程中产生的时间延迟因素,构建了一个含时滞的差异化双寡头Bertrand价格博弈模型。基于延迟有限理性决策及离散混沌模型稳定性分析方法,研究了该模型的动力学特性。通过分析系统的分岔图、混沌图以及各企业利润函数的变化探究该模型在纳什均衡点处系统的稳定性,研究了企业价格调整参数、产品差异化水平以及延迟权重系数对系统稳定性和企业利润的影响,为企业更好地理解和利用延迟提供有价值的理论参考和依据。(2)本文构建了一个具有延迟的双寡头企业主从型Bertrand价格博弈模型,利用有限理性准则及离散混沌模型稳定性分析方法,研究了该模型的动力学特性。通过分析系统的分岔图及各个企业利润的变化探究该模型在纳什均衡点处的稳定性,并且研究了延迟对系统稳定性以及企业利润的影响,从而为企业更好地理解和利用延迟提供有效参考。同时,基于MATLAB的数值仿真结果表明:企业价格调整速度(力度)的增大,会引起两企业价格演化的分岔现象,最终产生混沌行为;含有延迟的动力学系统与非延迟系统具有相同的纳什均衡点,并且延迟会增加系统的局部稳定域。(3)混沌状态不仅影响非线性动力系统的稳定性,也会影响企业的价格决策,导致企业利润随之产生剧烈波动,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,如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,这些措施均能够快速帮助混沌系统恢复到满足企业利润稳步增长的稳定状态。
[Abstract]:In recent years, with the wide application and promotion of the Internet and electronic commerce, consumers can hold all the price information of similar products without leaving the home. Therefore, under the premise of ensuring the quality of the products, The price advantage is more and more obvious in the market competition. In the past, the research on oligopoly competition in the market is mostly carried out around the production game, but there is little research on the price game. Therefore, this paper is based on the Bertrand model. On the basis of system stability theory and chaos theory, the dynamic characteristics and chaos control of price game among enterprises in oligopoly market competition are studied. In the face of the negative effects of these factors, what effective measures should be taken to suppress and eliminate these factors. This paper mainly completed the following three aspects of work. 1) based on the Bertrand price game model, Product difference is introduced to avoid the phenomenon of "Bertrand paradox", and the time delay factor in the process of pricing decision is considered. In this paper, a differential duopoly Bertrand price game model with time delay is constructed. Based on delay finite rational decision and stability analysis method of discrete chaotic model, the dynamic characteristics of the model are studied, and the bifurcation diagram of the system is analyzed. Study on the stability of the model at Nash equilibrium point, the effects of price adjustment parameters, product differentiation level and delay weight coefficient on system stability and corporate profits are studied. This paper constructs a Bertrand price game model of duopoly business owners with delay, which provides a valuable theoretical reference and basis for enterprises to better understand and utilize delay. The dynamic characteristics of the model are studied by using the finite rationality criterion and the stability analysis method of discrete chaotic model. The stability of the model at the Nash equilibrium point is investigated by analyzing the bifurcation diagram of the system and the changes of the profits of each enterprise. The effect of delay on system stability and corporate profit is also studied, which provides an effective reference for enterprises to better understand and utilize delay. At the same time, the numerical simulation results based on MATLAB show that the increase of enterprise price adjustment speed (intensity). The bifurcation of the price evolution of the two firms will result in chaotic behavior. The dynamical system with delay has the same Nash equilibrium point as the non-delay system. And the delay will increase the local stability of the system.) chaotic state will not only affect the stability of nonlinear dynamic system, but also affect the price decision of the enterprise, resulting in severe fluctuations in the profits of the enterprise, and becomes difficult to predict. In order to suppress and eliminate the influence of chaotic state, this paper uses the delayed feedback control method and the linear control method to control the chaotic state of the two models effectively, and puts forward several measures to help enterprises to implement feedback control. Such as controlling the speed of product price adjustment, reducing the product substitution rate, reducing the marginal cost of the product, choosing the appropriate delay weight coefficient, these measures can quickly help the chaotic system to recover to a stable state that satisfies the steady growth of the enterprise 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】:2016
【分类号】:F224.32;F726
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