Skip to main content
SpringerLink
Log in

The complex dynamics of R&D competition models of three oligarchs with heterogeneous players

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Aspremont, C., Jacquemin, A.: Cooperative and noncooperative R&D in duopoly with spillovers. Am. Econ. Rev. 78(5), 1133–1137 (1988)

    Google Scholar 

  2. Gersbach, H., Schmutzler, A.: External spillovers, internal spillovers and the geography of production and innovation. Reg. Sci. Urban Econ. 29(6), 679–696 (1999)

    Article  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. Luckraz, S.: R&D games in a Cournot duopoly with isoelastic demand functions: a comment. Econ. Model. 28(6), 2873–2876 (2011)

    Article  Google Scholar 

  5. Puu, T.: Complex dynamics with three oligopolists. Chaos Solitons Fractals 7(12), 2075–2081 (1996)

    Article  MathSciNet  Google Scholar 

  6. 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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Puu, T.: On the stability of Cournot equilibrium when the number of competitors increases. J. Econ. Behav. Organ. 66(3–4), 445–456 (2008)

    Article  Google Scholar 

  8. 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)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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)

    Article  MathSciNet  MATH  Google Scholar 

  10. Chen, Z.Q., Ip, W.H., Chan, C.Y., Yung, K.L.: Two-level chaos-based video cryptosystem on H.263 codec. Nonlinear Dyn. 62, 647–664 (2010)

    Article  Google Scholar 

  11. 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)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tramontana, F., Elsadany, A.A.: Heterogeneous triopoly game with isoelastic demand function. Nonlinear Dyn. 68(1), 187 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Ma, J.H., Ji, W.Zh.: Complexity of repeated game model in electric power triopoly. Chaos Solitons Fractals 40(4), 1735–1740 (2009)

    Article  MATH  Google Scholar 

  14. Zhang, J.L., Ma, J.H.: Research on the price game model for four oligarchs with different decision rules and its chaos control. Nonlinear Dyn. 70(1), 323–334 (2012)

    Article  Google Scholar 

  15. Sheng, Z.H., Li, Y., Chen, G.H.: Global complexity of RD dynamic competition model. J. Manag. Sci. China 9(3), 1–9 (2006)

    MathSciNet  Google Scholar 

  16. Hu, R., Chen, Q., Wang, Q.: Complexity analysis of dynamic R&D competition in duopoly. J. Ind. Eng. Manag. 25(2), 118–123 (2011)

    MathSciNet  Google Scholar 

  17. Luisa, M., Francesca, P., Randaccio, S.: Endogenous R&D and foreign direct investment in international oligopolies. Int. J. Ind. Organ. 18(2), 339–367 (2000)

    Article  Google Scholar 

  18. Li, C., Peng, J., Huang, Q.: Controlling synchronization of chaos and hyperchaos systems. J. Northeast. Norm. Univ. Nat. Sci. 33(3), 43–47 (2001)

    Google Scholar 

Download references

Acknowledgements

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).

Author information

Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Ting Li & Junhai Ma

  2. School of Economics and Management, Dezhou University, Dezhou, 253023, China

    Ting Li

Authors
  1. Ting Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junhai Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junhai Ma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, T., Ma, J. The complex dynamics of R&D competition models of three oligarchs with heterogeneous players. Nonlinear Dyn 74, 45–54 (2013). https://doi.org/10.1007/s11071-013-0947-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-013-0947-z

Keywords

Search

Navigation