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Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation

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  • Li, Yan
  • Wang, Lidong

Abstract

In this paper, we construct a duopoly model of technological innovation based on constant conjectural variation under the assumption of bounded rationality. The equilibrium points of constant conjectural variation and their local stability are investigated. By the theoretical proof, we prove that the model displays Li-Yorke chaos and distributional chaos in the ranges of the output adjusted coefficients by employing the snap-back repeller theory. The technological innovation is the main source of the core competitiveness of a firm, and technological content is an important factor of technological innovation. We find that the firms have the optimal technological contents while they could have the maximal profits in the two different situations, non-cooperative technological innovation and cooperative technological innovation. It’s proved that the cooperation of technological innovation can increase the marginal technological content, and benefit to technological progress. Then Numerical simulations are used to illustrate the dynamic analysis of the model under the situations with different technological innovation and conjectural variation. When the output adjusted coefficient changes, a series of complex phenomena including bifurcation, chaos and strange attractor can be observed in our model. And when the technological content is larger, the chaos of the system finally appears.

Suggested Citation

  • Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:116-126
    DOI: 10.1016/j.chaos.2018.11.038
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    1. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    2. d'Aspremont, Claude & Jacquemin, Alexis, 1990. "Cooperative and Noncooperative R&D in Duopoly with Spillovers: Erratum," American Economic Review, American Economic Association, vol. 80(3), pages 641-642, June.
    3. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    4. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
    5. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    6. Shinji Kobayashi, 2015. "On a Dynamic Model of Cooperative and Noncooperative R and D in Oligopoly with Spillovers," Dynamic Games and Applications, Springer, vol. 5(4), pages 599-619, December.
    7. Yu, Weisheng & Yu, Yu, 2014. "A dynamic duopoly model with bounded rationality based on constant conjectural variation," Economic Modelling, Elsevier, vol. 37(C), pages 103-112.
    8. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    9. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
    10. Furman, Jeffrey L. & Porter, Michael E. & Stern, Scott, 2002. "The determinants of national innovative capacity," Research Policy, Elsevier, vol. 31(6), pages 899-933, August.
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    6. Sameh S. Askar, 2020. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit," Mathematics, MDPI, vol. 8(10), pages 1-13, October.

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