Study on Complexity About a Category Three-Oligopoly System with R&D Investment Considering Multi-Factors
SUN Lijian1,2, MA Junhai1
1. College of Management and Economics, Tianjin University, Tianjin 300072, China; 2. College of Science, Tianjin University of Science and Technology, Tianjin 300457, China
Abstract:In this paper, a R&D input game model with spillovers, endogenous demand in a triopoly market is considered. All the players only get incomplete information and we assume they are all bounded rational. Two players make up a cooperative team, and share the technology achievements completely. On the basis of analyzing the stabilities of the only Nash equilibrium point, three-dimensional stable regions are investigated. The complex dynamics, such as bifurcation scenarios, route to chaos are displayed by 2D bifurcation diagrams. Impact of the adjustment speed, spillover rate and endogenous demand parameter on the profit is studied.
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.
[1] D’Aspremont C, Jacquemin A. Cooperative and noncooperative R&D in a duopoly with spillover[J].American Economic Review, 1988, 78(5): 1133-1137. [2] 霍沛军.一类单边堆积R&D模型的利润函数[J].系统工程学报,2002,17(5):451-457. Huo Peijun. Profit functions of a class of unilateral stochastic R&D model[J] Journal of Systems Engineering,2002,17(5):451-457. [3] Gersbach H, Schmutzler A. External spillovers, internal spillovers and the geography of production and innovation[J].Regional Science and Urban Economics, 1999, 29(6): 679-696. [4] Femminis G, Martini G. Irreversible investment and R & D spillovers in a dynamic duopoly[J].Journal of Economic Dynamics & Control, 2011,35(7): 1061-1090. [5] Vandekerckhove J, Bondt R De. Asymmetric spillovers and investments in research and development of leaders and followers[J].Economics of Innovation and New Technology, 2008, 17(5): 417-433. [6] Dawid H, Kopel. M, Kort P M. R&D competition versus R&D cooperation in oligopolistic markets with evolving structure[J].International Journal of Industrial Organization, 2013,31(5): 527-537. [7] Goel R K, Haruna S. Cooperative and noncooperative R&D with spillovers: the case of labor-managed firms[J].Economic Systems, 2007,31(4): 423-440. [8] Breton M, Turki A, Zaccour G. Dynamic model of R&D, spillovers, and efficiency of bertrand and cournot equilibria[J].J of Optimization Theory and Applications, 2004, 123(1): 1-25. [9] Cellini R, Lambertini L. Dynamic R&D with spillovers: competition vs cooperation[J].J of Economic Dynamic & Control, 2009, 33(3): 568-582. [10] 胡荣,陈 圻,王 强. 双寡头动态R&D竞争的复杂性研究[J].管 理 工 程 学 报,2011, 25(2): 118-123. Hu Rong,Chen Qi,Wang Qiang. Complex research on the duopoly dynamic R&D competition.[J].Journal of Industrial Engineering Management,2011,25(2):118-123. [11] 盛昭瀚,李煜,陈国华,等.企业R&D投入动态竞争系统的全局复杂性分析[J].管理科学学报. 2006,9(3):1-10. Sheng Zhaohan, LiYu, Chen Guohua, Global complexity of a R & D dynamic competition model[J].Journal of Management Sciences in China,2006,9(3):1-10. [12] 吴可菲,马军海. 异质双寡头R&D竞争的复杂性分析[J].复杂系统与复杂性科学, 2013,10(1):68-74. Wu Kefei, Ma Junhai. Complexity analysis on dynamic R&D competition of heterogeneous duopoly[J].Complex Systems and Complexity Science, 2013,10(1):68-74. [13] Li T, Ma J. The complex dynamics of R&D competition models of three oligarchs with heterogeneous players[J].Nonlinear Dyn, 2013, 74(1/2): 45-54. [14] Jason A C, Gallas. The structure of infinite periodic and chaotic hub cascades in phase diagrams of simple autonomous flows[J].International Journal of Bifurcation and Chaos, 2010,20(2): 197-211. [15] Ma J H, Wang H W. Complexity analysis of dynamic noncooperative game models for closed-loop supply chain with product recovery[J].Applied Mathematical Modelling. 2014,38(23): 5562-5572. [16] Ma J H, Guo Z B. The parameter basin and complex of dynamic game with estimation and two-stage consideration[J].Applied Mathematics and Computation, 2014, 248(1): 131-142. [17] Fanti L, Gori L, Sodini M. Nonlinear dynamics in a cournot duopoly with different attitudes towards strategic uncertainty[J].Abstract and Applied Analysis, 2013, (4): 11.