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Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products

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  • Naimzada, A.K.
  • Tramontana, F.

Abstract

In this paper we consider a Cournot–Bertrand duopoly model with linear demand and cost functions and with product differentiation. We propose a dynamic framework for the study of the stability properties of this kind of mixed oligopoly game, a rather neglected topic in the existing literature despite its relevance. In particular, in this paper we highlight the role of best response dynamics and of an adaptive adjustment mechanism for the stability of the equilibrium.

Suggested Citation

  • Naimzada, A.K. & Tramontana, F., 2012. "Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products," Economic Modelling, Elsevier, vol. 29(4), pages 1436-1439.
    • Handle: RePEc:eee:ecmode:v:29:y:2012:i:4:p:1436-1439
    DOI: 10.1016/j.econmod.2012.02.016
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    References listed on IDEAS

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    1. Piercarlo Zanchettin, 2006. "Differentiated Duopoly with Asymmetric Costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(4), pages 999-1015, December.
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    4. Tremblay, Carol Horton & Tremblay, Victor J., 2011. "The Cournot-Bertrand model and the degree of product differentiation," Economics Letters, Elsevier, vol. 111(3), pages 233-235, June.
    5. Arya, Anil & Mittendorf, Brian & Sappington, David E.M., 2008. "Outsourcing, vertical integration, and price vs. quantity competition," International Journal of Industrial Organization, Elsevier, vol. 26(1), pages 1-16, January.
    6. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
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    Citations

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    Cited by:

    1. Michael Kopel & Eva Maria Putz, 2021. "Information sharing in a Cournot–Bertrand duopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(7), pages 1645-1655, October.
    2. Villena, Marcelo J. & Araneda, Axel A., 2017. "Dynamics and stability in retail competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 37-53.
    3. Askar, S.S., 2022. "Nonlinear dynamic investigations and global analysis of a Cournot duopoly game with two different objectives," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    5. S. S. Askar & Mona F. EL-Wakeel & M. A. Alrodaini, 2018. "Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products," Complexity, Hindawi, vol. 2018, pages 1-13, February.
    6. Bian, Junsong & Lai, Kin Keung & Hua, Zhongsheng & Zhao, Xuan & Zhou, Guanghui, 2018. "Bertrand vs. Cournot competition in distribution channels with upstream collusion," International Journal of Production Economics, Elsevier, vol. 204(C), pages 278-289.
    7. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.
    8. Chang Ray-Yun & Hu Jin-Li & Lin Yan-Shu, 2018. "The Choice of Prices versus Quantities under Outsourcing," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(2), pages 1-20, July.
    9. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    10. Han, Bing & Chouinard, Hayley H., 2014. "Product quality, advertising intensity and market size," Economics Letters, Elsevier, vol. 124(2), pages 215-218.
    11. Chen, Xingli & Zhou, Jianheng, 2021. "The complexity analysis and chaos control in omni-channel supply chain with consumer migration and advertising cost sharing," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    12. Askar, S.S., 2022. "On the dynamics of Cournot duopoly game with private firms: Investigations and analysis," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    13. Anne-Christine Barthel & Eric Hoffmann, 2020. "On the existence and stability of equilibria in N-firm Cournot–Bertrand oligopolies," Theory and Decision, Springer, vol. 88(4), pages 471-491, May.
    14. Ray-Yun Chang & Yan-Shu Lin & Jin-Li Hu, 2015. "Mixed Competition and Patent Licensing," Australian Economic Papers, Wiley Blackwell, vol. 54(4), pages 229-249, December.
    15. Puu, Tonu & Tramontana, Fabio, 2019. "Can Bertrand and Cournot oligopolies be combined?," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 97-107.
    16. Elias Asproudis & Eleftherios Filippiadis, 2021. "Environmental Technological Choice in a Cournot-Bertrand Model," Journal of Industry, Competition and Trade, Springer, vol. 21(1), pages 43-58, March.
    17. Anne-Christine Barthel & Eric Hoffmann, 2019. "Rationalizability and learning in games with strategic heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 565-587, April.
    18. 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.
    19. Junhai Ma & Weiya Di & Hao Ren, 2017. "Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service," Complexity, Hindawi, vol. 2017, pages 1-12, September.
    20. Sameh Askar & Abdulaziz Foul & Tarek Mahrous & Saleh Djemele & Emad Ibrahim, 2021. "Global and Local Analysis for a Cournot Duopoly Game with Two Different Objective Functions," Mathematics, MDPI, vol. 9(23), pages 1-14, December.
    21. S. Askar, 2014. "On Cournot–Bertrand competition with differentiated products," Annals of Operations Research, Springer, vol. 223(1), pages 81-93, December.

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    More about this item

    Keywords

    Cournot–Bertrand model; Product differentiation; Stability; Dynamics; Oligopoly theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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