异质三寡头模型的R&D竞争分析

doi:10.3969/j.issn.1007-7375.2020.06.019

工业工程 ›› 2020, Vol. 23 ›› Issue (6): 138-145.doi: 10.3969/j.issn.1007-7375.2020.06.019

异质三寡头模型的R&D竞争分析

刘荣荣¹, 周伟¹, 柏恩鹏²

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

收稿日期:2019-09-19 发布日期:2020-12-18
作者简介:刘荣荣(1995-)，女，山东省人，硕士研究生，主要研究方向为经济系统的复杂性
基金资助:
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)

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

LIU Rongrong¹, ZHOU Wei¹, BAI Enpeng²

1. College of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China;
2. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2019-09-19 Published:2020-12-18

摘要/Abstract

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。

关键词: 三寡头, 异质产品, 技术溢出, 分岔, 多稳态

Abstract: 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.

Key words: three-oligarch, heterogeneous products, technology spillover, bifurcation, multistability

中图分类号:

F224

刘荣荣, 周伟, 柏恩鹏. 异质三寡头模型的R&D竞争分析[J]. 工业工程, 2020, 23(6): 138-145.

LIU Rongrong, ZHOU Wei, BAI Enpeng. An R&D Competition Analysis of Heterogeneous Three-oligarch Model[J]. Industrial Engineering Journal, 2020, 23(6): 138-145.

参考文献

[1] ELSADANY A A. A dynamic Cournot duopoly model with different strategies[J]. Journal of the Egyptian Mathematical Society, 2015, 23(1): 56-61
[2] ELSADANY A A. Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization[J]. Applied Mathematics and Computation, 2017, 294: 253-263
[3] BISCHI G I, LAMANTIA F, RADI D. An evolutionary Cournot model with limited market knowledge[J]. Journal of Economic Behavior & Organization, 2015, 116: 219-238
[4] FANTI L, GORI L, MAMMANA C, et al. Market share delegation in a Bertrand duopoly: synchronisation and multistability[J]. Discrete Dynamics in Nature and Society, 2015(2): 1-13
[5] FANTI L, GORI L, MAMMANA C, et al. Multistability and complex basins in a nonlinear duopoly with price competition and relative profit delegation[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2016, 26(9): 093110_1-093110_17
[6] AGLIARI A, NAIMZADA A, PECORA N. Nonlinear dynamics of a Cournot duopoly game with differentiated products[J]. Applied Mathematics and Computation, 2016, 281: 1-15
[7] GAO L, WANG Z, PANSINI R, et al. Collective punishment is more effective than collective reward for promoting cooperation[J]. Scientific Reports, 2016, 5: 17752_1-17752_12
[8] D'ASPREMONT, JACQUEMIN. Cooperative and noncooperative R&D in a duopoly with spillover[J]. American Economic Review, 1988, 78(5): 1133-1137
[9] SUZUMURA K. Cooperative and noncooperative R&D in an oligopoly with spillovers[J]. American Economic Review, 1992, 82(5): 1307-1320
[10] 姜林. 合作与非合作情形下的R&D战略投资[J]. 四川师范学院学报(自然科学版), 2002, 23(2): 118-123
JIANG Lin. The R&D stragetic investment with cooperation and noncooperation[J]. Journal of Sichuan Teachers College (Natural Science), 2002, 23(2): 118-123
[11] ZANG I, KAMIEN M I. Meet me halfway: research joint ventures and absorptive capacity[J]. International Journal of Industrial Organization, 2000, 18(7): 995-1012
[12] BISCHI G I, LAMANTIA F. A dynamic model of oligopoly with R&D externalities along networks. Part I[J]. Mathematics and Computers in Simulation, 2012, 84: 51-65
[13] BISCHI G I, LAMANTIA F. A dynamic model of oligopoly with R&D externalities along networks. Part II[J]. Mathematics and Computers in Simulation, 2012, 84: 66-82
[14] LI T, MA J. The complex dynamics of R&D competition models of three oligarchs with heterogeneous players[J]. Nonlinear Dynamics, 2013, 74(1-2): 45-54
[15] 孙立建, 马军海. 考虑多种因素的一类三寡头R&D投入系统复杂性研究[J]. 复杂系统与复杂性科学, 2016, 13(4): 80-89
SUN Lijian, MA Junhai. Study on complexity about a category three-oligopoly system with R&D investment considering multi-factors[J]. Complex Systems and Complexity Science, 2016, 13(4): 80-89
[16] ZHANG Y H, ZHOU W, CHU T, et al. Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production[J]. Nonlinear Dynamics, 2018, 91: 819-835
[17] ZHOU J, ZHOU W, CHU T, et al. Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R& D spillover and product differentiation[J]. Applied Mathematics and Computation, 2019, 341: 358-378

异质三寡头模型的R&D竞争分析

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

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

[1]	植璟涵，张光宇. 基于技术溢出与吸收能力的双寡头企业研发微分博弈分析[J]. 工业工程, 2015, 18(2): 94-99.
[2]	李卫红1，2, 白杨1. 竞争供应链R&D投资策略与协同机制研究[J]. 工业工程, 2013, 16(2): 80-86.