IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v29y2012i4p1436-1439.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S026499931200051X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2012.02.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    2. Piercarlo Zanchettin, 2006. "Differentiated Duopoly with Asymmetric Costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(4), pages 999-1015, December.
    3. 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.
    4. Koji Okuguchi, 1970. "Adaptive Expectations in an Oligopoly Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 233-237.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    3. 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.
    4. Han, Bing & Chouinard, Hayley H., 2014. "Product quality, advertising intensity and market size," Economics Letters, Elsevier, vol. 124(2), pages 215-218.
    5. 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.
    6. 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).
    7. 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).
    8. 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).
    9. 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.
    10. 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.
    11. Hsiao-Chi Chen & Yunshyong Chow & Shi-Miin Liu, 2024. "Dynamics of Cournot and Bertrand Firms: Exploring Imitation and Replicator Processes," Dynamic Games and Applications, Springer, vol. 14(5), pages 1057-1092, November.
    12. Puu, Tonu & Tramontana, Fabio, 2019. "Can Bertrand and Cournot oligopolies be combined?," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 97-107.
    13. Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    14. Nálepová, Veronika & Lampart, Marek, 2024. "Impact of windfall tax on market dynamics: A Cournot oligopoly model with exogenous shocks," Economic Modelling, Elsevier, vol. 137(C).
    15. 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.
    16. 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.
    17. Ahmed, Rizwan & Qureshi, M. Zubair Akbar & Abbas, Muhammad & Mumtaz, Nida, 2025. "Bifurcation and chaos control in a heterogeneous Cournot-Bertrand duopoly game model," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    18. 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.
    19. 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.
    20. 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.
    21. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.
    22. 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.
    23. 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.
    24. S. Askar, 2014. "On Cournot–Bertrand competition with differentiated products," Annals of Operations Research, Springer, vol. 223(1), pages 81-93, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Olga Rozanova, 2017. "The possibility to renegotiate the contracts and the equilibrium mode of competition in vertically related markets," Economics Bulletin, AccessEcon, vol. 37(3), pages 1573-1580.
    2. Hsiao‐Chi Chen & Shi‐Miin Liu & Sung‐Chi Lin, 2023. "Spatial agglomeration or dispersion under Cournot‐Bertrand competition," Manchester School, University of Manchester, vol. 91(5), pages 414-438, September.
    3. 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.
    4. S. Askar, 2014. "On Cournot–Bertrand competition with differentiated products," Annals of Operations Research, Springer, vol. 223(1), pages 81-93, December.
    5. Arijit Mukherjee & Burcu Senalp, 2024. "Complementary inputs, outsourcing and vertical integration: Price versus quantity competition," Manchester School, University of Manchester, vol. 92(5), pages 578-611, September.
    6. Ciprian Rusescu & Mihai Daniel - Roman, 2021. "Dynamic Behaviour In A Bertrand Model With Bounded Rational Players," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 3, pages 45-55, June.
    7. Ryo Sakamoto & Kyle Stiegert, 2018. "Comparing competitive toughness to benchmark outcomes in retail oligopoly pricing," Agribusiness, John Wiley & Sons, Ltd., vol. 34(1), pages 44-60, December.
    8. Ki‐Dong Lee & Kangsik Choi, 2024. "Uniform versus discriminatory tariffs when competition mode is endogenous," Bulletin of Economic Research, Wiley Blackwell, vol. 76(1), pages 95-120, January.
    9. 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.
    10. Lee, DongJoon & Choi, Kangsik & Nariu, Tatsuhiko, 2016. "Endogenous Choice of Price or Quantity Contract with Upstream R&D Investment: Linear Pricing and Two-part Tariff Contract with Bargaining," MPRA Paper 72752, University Library of Munich, Germany.
    11. Chia-Jen Chang & Chih-Ta Yen & Yu-Zhen Lin, 2024. "Commodity taxation principle, heterogeneous goods, and endogenous choice between price and quantity contracts," Journal of Economics, Springer, vol. 143(2), pages 111-140, October.
    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. Manasakis, Constantine & Vlassis, Minas, 2014. "Downstream mode of competition with upstream market power," Research in Economics, Elsevier, vol. 68(1), pages 84-93.
    14. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    15. Hsiao-Chi Chen & Yunshyong Chow & Shi-Miin Liu, 2024. "Dynamics of Cournot and Bertrand Firms: Exploring Imitation and Replicator Processes," Dynamic Games and Applications, Springer, vol. 14(5), pages 1057-1092, November.
    16. Mukherjee, Arijit & Wang, Leonard F.S. & Sun, Ji, 2024. "Bertrand-Cournot profit reversal in a vertical structure with cross ownership," Economics Letters, Elsevier, vol. 238(C).
    17. Kangsik Choi & Seonyoung Lim, 2023. "Input Price Discrimination in Endogenous Competition Mode," The Japanese Economic Review, Springer, vol. 74(2), pages 301-330, April.
    18. José Méndez‐Naya & José A. Novo‐Peteiro, 2023. "Partial privatization with endogenous choice of strategic variable," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(2), pages 1215-1227, March.
    19. Montinaro, Marta & Scrimitore, Marcella, 2019. "Per unit and ad valorem royalties in a patent licensing game," MPRA Paper 96642, University Library of Munich, Germany.
    20. Li, Changying & Ji, Xiaoming, 2010. "Innovation, licensing, and price vs. quantity competition," Economic Modelling, Elsevier, vol. 27(3), pages 746-754, May.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecmode:v:29:y:2012:i:4:p:1436-1439. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.