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The dynamics of a differentiated duopoly with quantity competition

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  • Fanti, Luciano
  • Gori, Luca

Abstract

We analyse the dynamics of a Cournot duopoly game with heterogeneous players to investigate the effects of micro-founded differentiated products demand. The present analysis, which modifies and extends Zhang et al. (2007) (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148) and Tramontana, F., (2010) (Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357), reveals that a higher degree of product differentiation may destabilise the market equilibrium. Moreover, we show that a cascade of flip bifurcations may lead to periodic cycles and ultimately chaotic motions. Since a higher degree of product differentiation implies weaker competition, then a theoretical implication of our findings, that also constitute a policy warning for firms, is that a fiercer (weaker) competition tends to stabilise (destabilise) the unique positive Cournot-Nash equilibrium of the economy.

Suggested Citation

  • Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a differentiated duopoly with quantity competition," MPRA Paper 33477, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:33477
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    References listed on IDEAS

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    Cited by:

    1. Joaquín Andaluz & Gloria Jarne, 2016. "Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational," Annals of Operations Research, Springer, vol. 238(1), pages 1-25, March.
    2. Fanti, Luciano, 2014. "The dynamics of a banking duopoly with capital regulations," Economic Modelling, Elsevier, vol. 37(C), pages 340-349.
    3. Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
    4. Luciano Fanti, 2015. "Environmental Standards and Cournot Duopoly: A Stability Analysis," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 61(4), pages 577-593, August.
    5. Fanti, Luciano & Gori, Luca, 2012. "The codetermined firm in a Cournot duopoly: A stability analysis," Economic Modelling, Elsevier, vol. 29(4), pages 1242-1247.
    6. César García-Díaz & Gábor Péli & Arjen van Witteloostuijn, 2020. "The coevolution of the firm and the product attribute space," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-25, June.
    7. Yu Yu & Weisheng Yu, 2019. "The Complexion of Multi-period Stackelberg Triopoly Game with Bounded Rationality," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 457-478, January.
    8. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    9. Joaquín Andaluz & Gloria Jarne, 2016. "Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational," Annals of Operations Research, Springer, vol. 238(1), pages 1-25, March.
    10. Li, Wen-na & Elsadany, A.A. & Zhou, Wei & Zhu, Yan-lan, 2021. "Global Analysis, Multi-stability and Synchronization in a Competition Model of Public Enterprises with Consumer Surplus," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. Yu, Weisheng & Yu, Yu, 2014. "The complexion of dynamic duopoly game with horizontal differentiated products," Economic Modelling, Elsevier, vol. 41(C), pages 289-297.
    12. Askar, S.S. & Alshamrani, Ahmad M. & Alnowibet, K., 2015. "Dynamic Cournot duopoly games with nonlinear demand function," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 427-437.
    13. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.
    14. Andaluz, J. & Elsadany, A.A. & Jarne, G., 2017. "Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 86-99.
    15. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    16. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    17. Baogui Xin & Wei Peng & Yekyung Kwon, 2019. "A fractional-order difference Cournot duopoly game with long memory," Papers 1903.04305, arXiv.org.
    18. Du, Jian-guo & Fan, Yue-qian & Sheng, Zhao-han & Hou, Yun-zhang, 2013. "Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter," Economic Modelling, Elsevier, vol. 33(C), pages 507-516.
    19. PAPADOPOULOS Kosmas & SARAFOPOULOS Georges, 2019. "Dynamics of a Cournot Game with Differentiated Goods and Asymmetric Cost Functions based on Relative Profit Maximization," European Journal of Interdisciplinary Studies, Bucharest Economic Academy, issue 02, June.
    20. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    21. Agliari, A. & Naimzada, A.K. & Pecora, N., 2016. "Nonlinear dynamics of a Cournot duopoly game with differentiated products," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 1-15.
    22. Fanti, Luciano & Gori, Luca, 2011. "Cross-ownership and stability in a Cournot duopoly," MPRA Paper 34574, University Library of Munich, Germany.
    23. Joaquín Andaluz & Gloria Jarne, 2019. "On price stability and the nature of product differentiation," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 741-762, April.

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    More about this item

    Keywords

    Bifurcation; Chaos; Cournot; Oligopoly; Product differentiation;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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