基于创新驱动的天然气三寡头垄断市场动态微分博弈定价模型
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摘要
针对天然气生产商三寡头垄断市场,基于知识创新所产生的成本降低和降价决策反应时滞,建立了定价决策动态微分博弈模型.模型分析发现:知识创新周期不变时,企业可通过调整知识创新投入产出强度来降低成本,并据此实施降价策略,随着创新投入产出强度的改变,系统会出现Hopf分岔,且有唯一的Nash平衡点;当创新投入产出强度不断增加时,系统会达到并保持平衡状态;而创新投入产出强度不断降低时,系统会出现周期解,进而增大周期运动幅度,市场出现无序竞争状态.数值模拟印证了理论推导结果.该研究对于三寡头垄断市场中,各天然气生产商有效实施创新驱动战略具有积极的参考价值.
The triopoly market of natural gas manufacturers was studied,and a dynamic differential game pricing model was established based on the cost reduction resulting from knowledge innovation and the response lag in the price reduction decision. Model analyses indicate that,when the period of knowledge innovation remains constant,enterprises can reduce costs by adjusting the input and output intensities of knowledge innovation and implement price strategies accordingly. With the variation of the input and output intensities of knowledge innovation,the Hopf bifurcation and a single Nash equilibrium point will emerge in the system. With continuous increases of the input and output intensities,the system will reach and maintain an equilibrium; with continuous decreases of the input and output intensities,the system will yield a periodic solution,the range of the periodic motion will expand,and the market will fall into a chaotic competitive state. Numerical simulations confirm the theoretically derived results. This study provides a reference for the natural gas manufacturers within the triopoly market to effectively implement innovation-driven strategies.
The triopoly market of natural gas manufacturers was studied,and a dynamic differential game pricing model was established based on the cost reduction resulting from knowledge innovation and the response lag in the price reduction decision. Model analyses indicate that,when the period of knowledge innovation remains constant,enterprises can reduce costs by adjusting the input and output intensities of knowledge innovation and implement price strategies accordingly. With the variation of the input and output intensities of knowledge innovation,the Hopf bifurcation and a single Nash equilibrium point will emerge in the system. With continuous increases of the input and output intensities,the system will reach and maintain an equilibrium; with continuous decreases of the input and output intensities,the system will yield a periodic solution,the range of the periodic motion will expand,and the market will fall into a chaotic competitive state. Numerical simulations confirm the theoretically derived results. This study provides a reference for the natural gas manufacturers within the triopoly market to effectively implement innovation-driven strategies.
引文
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[2]杨世旭,段万春,孙永河,等.基于混合策略的电信企业竞合博弈分析[J].经济问题探索,2014(8):179-183.(YANG Shixu,DUAN Wanchun,SUN Yonghe,et al. An analysis of the competition and merger game of telecommunications enterprises based on a mixed strategy[J]. Inquiry Into Economic Issues,2014(8):179-183.(in Chinese))
[3]吉伟卓,马军海.发电市场不同决策规则三寡头博弈模型研究[J].系统工程学报,2008,23(3):257-263.(JI Weizhuo,MA Junhai. Study of game model based on different decision rules in electric power triopoly market[J]. Journal of Systems Engineering,2008,23(3):257-263.(in Chinese))
[4] ELABBASY E M,AGIZA H N,ELSADANY A A. Analysis of nonlinear triopoly game with heterogeneous players[J]. Computers&Mathematics With Applications,2009,57(3):488-499.
[5] CHEN F,MA J H,CHEN X Q. The study of dynamic process of the triopoly games in Chinese3G telecommunication market[J]. Chaos,Solitons&Fractals,2009,42(3):1542-1551.
[6] MA J H,JI W Z. Complexity of repeated game model in electric power triopoly[J]. Chaos,Solitons&Fractals,2009,40(4):1735-1740.
[7] AGIZA H N,HEGAZI A S,ELSADANY A A. The dynamics of Bowley’s model with bounded rationality[J]. Chaos,Solitons&Fractals,2001,12(9):1705-1717.
[8]谢英超,程燕,贺天宇.一类具有非线性发生率的时滞传染病模型的全局稳定性[J].应用数学和力学,2015,36(10):1107-1116.(XIE Yingchao,CHENG Yan,HE Tianyu. Global stability of a class of delayed epidemic models with nonlinear incidence rates[J]. Applied Mathematics and Mechanics,2015,36(10):1107-1116.(in Chinese))
[9]孙继涛,王庆国,高含俏.具有时变滞后的随机系统的时滞依赖鲁棒稳定性与H∞分析[J].应用数学和力学,2010,31(2):236-244.(SUN Jitao,WANG Qingguo,GAO Hanqiao. Delay-dependent robust stability and H∞analysis of stochastic systems with time-varying delay[J]. Applied Mathematics and Mechanics,2010,31(2):236-244.(in Chinese))
[10]高琴.港口产业集群的复杂性研究[D].博士学位论文.天津:天津大学,2009.(GAO Qin. The research of the complexity of port industrial clusters[D]. PhD Thesis. Tianjin:Tianjin University,2009.(in Chinese))
[11] SON W S,PARK Y J. Delayed feedback on the dynamical model of a financial system[J]. Chaos,Solitons&Fractals,2011,44(4):208-217.
[12]徐伟,马军海.保险市场中三寡头垄断的动态博弈模型研究[J].复杂系统与复杂性科学,2013,10(2):52-58.(XU Wei,MA Junhai. Study on the dynamical model of a triopoly game in insurance market[J]. Complex Systems and Complexity Science,2013,10(2):52-58.(in Chinese))
[13]杨俊,张亚军,张小漫.天然气市场不同预期规则下的三寡头博弈模型研究[J].华东经济管理,2016,30(8):7-15.(YANG Jun,ZHANG Yajun,ZHANG Xiaoman. A study of three oligopolistic firms game model based on different expectation rules in natural gas supply market[J]. East China Economic Management,2016,30(8):7-15.(in Chinese))
[14] RAYPORT J F,SVIOKLA J J. Exploiting the virtual value chain[J]. Harvard Business Review,1995,73(6):75-85.
[15]赵小惠,陈菊红,孙林岩,等.制造商-供应商协同产品创新合作机制研究[J].工业工程,2005,8(6):60-63.(ZHAO Xiaohui,CHEN Juhong,SUN Linyan,et al. Cooperation mechanisms of collaboration product innovation for manufacturer-supplier[J]. Industrial Engineering Journal,2005,8(6):60-63.(in Chinese))
[16] DOCKNER E,JORGENSEN S,LONG N V,et al. Differential Games in Economics and Management Science[M]. Oxford:Cambridge University Press,2000.
[17] BAGCHI A. Stackelberg Differential Games in Economic Models[M]. Berlin:Springer Verlag,1984.
[18]张庶萍,张世英.基于微分对策的供应链合作广告决策研究[J].控制与決策,2006,21(2):153-157.(ZHANG Shuping,ZHANG Shiying. Dynamic cooperative advertising strategies based on differential games in a supply chain[J]. Control and Decision,2006,21(2):153-157.(in Chinese))
[19]胡震云,陈晨,张玮.基于微分博弈的绿色信贷与水污染控制反馈策略研究[J].审计与经济研究,2013,28(6):100-109.(HU Zhenyun,CHEN Chen,ZHANG Wei. Study on the feedback strategy of water pollution control differential game from the view of green credit[J]. Journal of Audit&Economics,2013,28(6):100-109.(in Chinese))
[20]郝晓晨.天然气产业链架构的和谐性分析与优化[J].天然气工业,2006,26(12):162-164.(HAO Xiaochen. Analysis and optimization on the integrity and harmony of natural gas industry chain[J]. Natural Gas Industry,2006,26(12):162-164.(in Chinese))
[21]白兰君.在对比研究中深入探寻油气采掘成本规律[J].天然气经济,2006(6):4-7.(BAI Lanjun.A profound probe into rules of oil and gas producing costs by comparative study[J]. Natural Gas Technology and Economy,2006(6):4-7.(in Chinese))
[22]潘玉荣,贾朝勇.不同理性双寡头博弈模型的复杂性分析[J].复杂系统与复杂性科学,2007,4(2):71-76.(PAN Yurong,JIA Chaoyong. Complex dynamics analysis for a duopoly game with heterogeneous players[J]. Complex Systems and Complexity Science,2007,4(2):71-76.(in Chinese))