This paper uses the theory of bifurcations of dynamical systems, considering R&D input competition model in oligopoly market with heterogeneous rationality. We assume that cooperation, as well as competition, exists among the oligarchs, which are closer to reality and different from previous studies. On the basis of analyzing the stabilities of four fixed points in the three-dimensional dynamic system, a local stable region of Nash equilibrium is obtained. Simulation results show that the adjustment of R&D input speed has an obvious impact on the complexity of competition, and also show that the system profit will decrease when it is in chaos. So this paper discusses the application of parameters control method when the model is in chaos and then allows the oligarchs to eliminate the negative effects.
Triopoly R&D competition Heterogeneous rationality Chaos control
This is a preview of subscription content, log in to check access.
This work was supported by the National Nature Science Foundation of China (No. 61273231) and the Doctoral Scientific Fund Project of the Ministry of Education of China (No. 20090032110031).
Aspremont, C., Jacquemin, A.: Cooperative and noncooperative R&D in duopoly with spillovers. Am. Econ. Rev. 78(5), 1133–1137 (1988)
Gersbach, H., Schmutzler, A.: External spillovers, internal spillovers and the geography of production and innovation. Reg. Sci. Urban Econ. 29(6), 679–696 (1999)
Milstein, T.: R&D wars and the effects of innovation on the success and survivability of firms in oligopoly markets. Int. J. Ind. Organ. 27(4), 519–531 (2009)
Luckraz, S.: R&D games in a Cournot duopoly with isoelastic demand functions: a comment. Econ. Model. 28(6), 2873–2876 (2011)
Puu, T., Marín, M.R.: The dynamics of a triopoly Cournot game when the competitors operate under capacity constraints. Chaos Solitons Fractals 28(2), 403–413 (2006)
Puu, T.: On the stability of Cournot equilibrium when the number of competitors increases. J. Econ. Behav. Organ. 66(3–4), 445–456 (2008)
Agiza, H.N., Hegazi, A.S., Elsadany, A.A.: Complex dynamics and synchronization of a duopoly game with bounded rationality. Math. Comput. Simul. 58(2), 133–146 (2002)
Agiza, H.N., Elsadany, A.A.: Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Phys. A, Stat. Mech. Appl. 320, 512–524 (2003)
Chen, Z.Q., Yang, Y., Yuan, Z.Z.: A single three-wing or four-wing chaotic attractor generated from a three dimensional smooth quadratic autonomous system. Chaos Solitons Fractals 38, 1187–1196 (2008)