异质三寡头模型的R&D竞争分析  

An R&D Competition Analysis of Heterogeneous Three-oligarch Model

作　　者：刘荣荣 周伟[1] 柏恩鹏 LIU Rongrong;ZHOU Wei;BAI Enpeng(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070 [2]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《工业工程》2020年第6期138-145,共8页Industrial Engineering Journal

基　　金：国家自然科学基金资助项目(61364001);兰州交通大学青年科学研究基金资助项目(2015029)。

摘　　要：建立一个生产异质产品的Bertrand三寡头动态模型,其中企业1和企业2组成研发联盟。利用稳定性判据对模型的稳定性进行理论分析,并通过数值仿真得出系统关于R&D调整速度的稳定域。同时讨论了R&D调整速度和技术溢出率的改变对R&D投入的影响。结果表明,随着R&D调整速度的增加,市场将丢失其稳定性;在企业3技术溢出率确定的情况下,研发联盟较小的技术溢出率反而不利于整个市场的稳定。对于多稳态的讨论得出,R&D调整速度的改变不仅会导致吸引盆大小以及形状的改变,还会导致吸引子状态的变化。A Bertrand three-oligarch dynamic model for producing heterogeneous products is established,in which firm1 and firm 2 form R&D alliance.The stability of the model is theoretically analyzed using the stability criterion and the stability region of the speed of R&D adjustment is obtained by numerical simulation.The influence of the change of the speed of R&D adjustment and technology spillover rate on R&D input is also discussed.The result shows that with the increase of the speed of R&D adjustment,the market will lose its stability.When the technology spillover rate of firm 3 is certain,the smaller technology spillover of the R&D alliance will not be conducive to the stability of the whole market.Finally,through the study of multistability,it is concluded that the state of attractors and the size or shape of the basin will change with the change of the speed of R&D adjustment.

关 键 词：三寡头 异质产品 技术溢出 分岔 多稳态 

分 类 号：F224[经济管理—国民经济]