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On Cournot–Bertrand competition with differentiated products

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  • S. Askar

Abstract

In this paper, we present a game theoretic framework for Cournot–Bertrand competition based on a nonlinear price function. The competition is between two firms and is assumed to take place in terms of pricing decision and quantity produced. However, the proposed objective function has not been used in literature before, yet the throughput obtained in this paper generalizes some of the existing results in literature. The competitive interaction between firms is described and analyzed using best-reply reaction, proposed adaptive adjustment and bounded rationality approach. The condition of stability of Nash equilibrium (NE) is induced by these approaches. Interestingly, we prove that there exists exactly a unique NE. Furthermore, it is noticed that when firms adopt best-reply and the proposed adaptive adjustment, the firms’ strategic variables become asymptotically stable. On the contrary, when the bounded rationality is used both quantity and price behave chaotically due to bifurcation occurred. Copyright Springer Science+Business Media New York 2014

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  • S. Askar, 2014. "On Cournot–Bertrand competition with differentiated products," Annals of Operations Research, Springer, vol. 223(1), pages 81-93, December.
  • Handle: RePEc:spr:annopr:v:223:y:2014:i:1:p:81-93:10.1007/s10479-014-1612-8
    DOI: 10.1007/s10479-014-1612-8
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    References listed on IDEAS

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    1. 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.
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    7. 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.
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    Cited by:

    1. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    2. Jian Ni & Lap Keung Chu & Shoude Li, 2018. "Financial hedging and competitive strategy for value-maximizing firms under quantity competition," Annals of Operations Research, Springer, vol. 264(1), pages 391-407, May.
    3. 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.
    4. Sung Hee Lee & Kun Soo Park & Yong Won Seo, 2016. "Multinational Firm’s Production Decisions under Overlapping Free Trade Agreements: Rule of Origin Requirements and Environmental Regulation," Sustainability, MDPI, Open Access Journal, vol. 9(1), pages 1-16, December.
    5. 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.
    6. 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.
    7. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Askar, S.S. & Alshamrani, Ahmad M. & Alnowibet, K., 2016. "The arising of cooperation in Cournot duopoly games," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 535-542.
    13. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.

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