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

doi:10.3969/j.issn.1007-7375.2020.06.019

Abstract

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

CLC Number:

F224

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.

References

[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