基于低碳技术转让的寡头企业价格博弈的稳定性分析
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摘要
在考虑低碳技术转让的基础上,建立带时滞的动态双寡头价格博弈模型,分析模型Hopf分岔的存在性,给出系统局部渐近稳定性的条件,探究时滞参数、价格调整速度和低碳技术转让程度对系统稳定性的影响。研究表明,时滞参数和价格调整速度必须在合理的范围内变动,否则易使系统失稳;低碳技术转让程度越高,其自身利益受损越严重。
Considering the transfer of low-carbon technology,a dynamic duopoly price game model with delays is established. The existence of Hopf bifurcation is analyzed and the conditions of local asymptotic stability are given. The impact of delay parameters,price adjustment speed and low carbon technology transfer degree on system stability is explored. The research shows that the delay parameters and price adjustment speed must be within a reasonable range,otherwise the system will be easily unstable; the higher the degree of transfer of low-carbon technology,the more serious the damage to its own profits.
Considering the transfer of low-carbon technology,a dynamic duopoly price game model with delays is established. The existence of Hopf bifurcation is analyzed and the conditions of local asymptotic stability are given. The impact of delay parameters,price adjustment speed and low carbon technology transfer degree on system stability is explored. The research shows that the delay parameters and price adjustment speed must be within a reasonable range,otherwise the system will be easily unstable; the higher the degree of transfer of low-carbon technology,the more serious the damage to its own profits.
引文
[1]慕艳芬,马祖军,聂佳佳.碳税政策下竞争性企业低碳技术选择和技术许可研究[J].软科学,2017(9):115-119.
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[11]Kuznetsov Y A. Elements of applied bifurcation theory[M]. New York:Springer,2004.
[2]魏守道,周建波.碳税政策下供应链低碳技术研发策略选择[J].管理学报,2016(12):1834-1841.
[3]刘名武,万谧宇,付红.碳交易和低碳偏好下供应链低碳技术选择研究[J].中国管理科学,2018(1):152-162.
[4]蔡小哩,丁志刚,晚春东.供应链低碳技术采纳与产品定价协同决策研究[J].生态经济,2018(6):51-56,67.
[5]张雅慧,周伟,黄萌佳,等.基于延迟决策和溢出效应的双寡头博弈稳定性[J].兰州交通大学学报,2018(1):119-124.
[6]李金溪,易余胤.考虑产品节能激励的双寡头竞争博弈模型[J].计算机集成制造系统,2018(6):1522-1530.
[7]王琦玮,赵刘威,梅强,等.双寡头Bertrand博弈模型动态分析与混沌控制[J].统计与决策,2017(21):38-41.
[8]Luca Gori,Mauro Sodini. Price competition in a nonlinear differentiated duopoly[J]. Chaos,Solitons and Fractals,2017(104):557-567.
[9]Yue Xiao,Yu Peng,Qian Lu,et al. Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players[J].Physica A,2018(492):1980-1987.
[10]Chenghan Wu. Price competition and technology licensing in a dynamic duopoly[J]. European Journal of Operational Research,2018(267):570-584.
[11]Kuznetsov Y A. Elements of applied bifurcation theory[M]. New York:Springer,2004.