IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v274y2019i1d10.1007_s10479-018-2837-8.html
   My bibliography  Save this article

Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes

Author

Listed:
  • A. A. Elsadany

    (Prince Sattam Bin Abdulaziz University
    Suez Canal University)

  • A. M. Awad

    (Suez Canal University)

Abstract

This paper investigates the difference between price and quantity competition in a mixed duopoly game. We describe the behavior of a duopolistic Bertrand competition market with environmental taxes. There are two cases. In the first, the public firm is privatized and in the second, it is not privatized. In case I, private duopoly (postprivatization) where players use different production methods and choose their prices with (bounded rationality and naive). In case II, mixed duopoly (preprivatization) in this case there are two levels for the market including standard objective of the private firm is to maximize profits and including another objective function of the public firm namely “private welfare maximization”. We study numerically the dynamical behaviors of the models. The Nash equilibrium loses stability through a period-doubling bifurcation and the market in the end gets to be disordered. The disordered behavior of the market has been controlled by using feedback control method.

Suggested Citation

  • A. A. Elsadany & A. M. Awad, 2019. "Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes," Annals of Operations Research, Springer, vol. 274(1), pages 211-240, March.
    • Handle: RePEc:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2837-8
    DOI: 10.1007/s10479-018-2837-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-2837-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-018-2837-8?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. Wang, Leonard F.S. & Wang, Jean, 2009. "Environmental taxes in a differentiated mixed duopoly," Economic Systems, Elsevier, vol. 33(4), pages 389-396, December.
    2. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    3. Juan Carlos Bárcena‐Ruiz & Máximo Sedano, 2011. "Endogenous Timing In A Mixed Duopoly: Weighted Welfare And Price Competition," The Japanese Economic Review, Japanese Economic Association, vol. 62(4), pages 485-503, December.
    4. Trishita Bhattacharjee & Rupayan Pal, 2013. "Price vs. Quantity in duopoly with strategic delegation: Role of network externalities," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2013-010, Indira Gandhi Institute of Development Research, Mumbai, India.
    5. Sedano Hoyuelos, Máximo & Bárcena Ruiz, Juan Carlos, 2011. "Endogenous Timing in a Mixed Duopoly: Wighted Welfare and Price Competition," IKERLANAK 2011-46, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    6. 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.
    7. Chen, Fang & Ma, Jun Hai & Chen, Xiao Qiang, 2009. "The study of dynamic process of the triopoly games in chinese 3G telecommunication market," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1542-1551.
    8. Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    9. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
    10. Beladi, Hamid & Chao, Chi-Chur, 2006. "Does privatization improve the environment?," Economics Letters, Elsevier, vol. 93(3), pages 343-347, December.
    11. Ghosh, Arghya & Mitra, Manipushpak, 2010. "Comparing Bertrand and Cournot in mixed markets," Economics Letters, Elsevier, vol. 109(2), pages 72-74, November.
    12. Ahmed, E. & Elsadany, A.A. & Puu, Tonu, 2015. "On Bertrand duopoly game with differentiated goods," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 169-179.
    13. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2013. "The dynamics of a Bertrand duopoly with differentiated products: Synchronization, intermittency and global dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 73-86.
    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. 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).
    2. Zongxian Wang & Xiao Li & Weihua Liang & Junhai Ma, 2023. "Does a New Electric Vehicle Manufacturer Have the Incentive for Battery Life Investment? A Study Based on the Game Framework," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    3. Hongqiang Fan & Yichen Sun & Lifen Yun & Runfeng Yu, 2023. "A Joint Distribution Pricing Model of Express Enterprises Based on Dynamic Game Theory," Mathematics, MDPI, vol. 11(19), pages 1-17, September.
    4. Ma, Junhai & Hou, Yaming & Yang, Wenhui & Tian, Yi, 2020. "A time-based pricing game in a competitive vehicle market regarding the intervention of carbon emission reduction," Energy Policy, Elsevier, vol. 142(C).

    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. Xu, Lili & Cho, Sumi & Lee, Sang-Ho, 2016. "Emission tax and optimal privatization in Cournot–Bertrand comparison," Economic Modelling, Elsevier, vol. 55(C), pages 73-82.
    2. Toshihiro Matsumura & Akira Ogawa, 2014. "Corporate Social Responsibility or Payoff Asymmetry? A Study of an Endogenous Timing Game," Southern Economic Journal, John Wiley & Sons, vol. 81(2), pages 457-473, October.
    3. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    4. Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," MPRA Paper 33268, University Library of Munich, Germany.
    5. Luciano Fanti & Nicola Meccheri, 2015. "On the Cournot–Bertrand Profit Differential and the Structure of Unionisation in a Managerial Duopoly," Australian Economic Papers, Wiley Blackwell, vol. 54(4), pages 266-287, December.
    6. Junichi Haraguchi & Toshihiro Matsumura, 2020. "Endogenous public and private leadership with diverging social and private marginal costs," Manchester School, University of Manchester, vol. 88(5), pages 699-730, September.
    7. 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.
    8. Xu, Lili & Fan, Xinying & Luan, Weixin, 2020. "Strategic corporate social responsibility of high-speed rail in China," China Economic Review, Elsevier, vol. 62(C).
    9. Fanti, Luciano, 2013. "Cross-ownership and unions in a Cournot duopoly: When profits reduce with horizontal product differentiation," Japan and the World Economy, Elsevier, vol. 27(C), pages 34-40.
    10. Ohnishi, Kazuhiro, 2019. "Capacity choice in an international mixed triopoly," MPRA Paper 94051, University Library of Munich, Germany.
    11. Yasuhiko Nakamura, 2015. "Endogenous Choice of Strategic Variables in an Asymmetric Duopoly with Respect to the Demand Functions that Firms Face," Manchester School, University of Manchester, vol. 83(5), pages 546-567, September.
    12. Manipushpak Mitra & Rupayan Pal & Arindam Paul & P. M. Sharada, 2020. "Equilibrium Coexistence of Public and Private Firms and the Plausibility of Price Competition," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 176(2), pages 217-242.
    13. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2014. "Local and global dynamics in a duopoly with price competition and market share delegation," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 253-270.
    14. Kazuhiro Ohnishi, 2022. "Lifetime Employment and Stackelberg Mixed Duopoly Games with a Foreign Labour-Managed Competitor," Arthaniti: Journal of Economic Theory and Practice, , vol. 21(1), pages 27-42, June.
    15. Haraguchi, Junichi & Matsumura, Toshihiro, 2014. "Price versus quantity in a mixed duopoly with foreign penetration," Research in Economics, Elsevier, vol. 68(4), pages 338-353.
    16. Kosuke Hirose & Toshihiro Matsumura, 2019. "Comparing welfare and profit in quantity and price competition within Stackelberg mixed duopolies," Journal of Economics, Springer, vol. 126(1), pages 75-93, January.
    17. Xu, Lili & Matsumura, Toshihiro, 2022. "Welfare-reducing price competition under relative performance delegation with convex costs," Economic Modelling, Elsevier, vol. 112(C).
    18. Pal, Rupayan & Saha, Bibhas, 2015. "Pollution tax, partial privatization and environment," Resource and Energy Economics, Elsevier, vol. 40(C), pages 19-35.
    19. Xu, Lili & Chen, Yuyan & Lee, Sang-Ho, 2022. "Emission tax and strategic environmental corporate social responsibility in a Cournot–Bertrand comparison," Energy Economics, Elsevier, vol. 107(C).
    20. Rupayan Pal, "undated". "The Cournot-Bertrand profit differential: A Reversal result in network goods duopoly," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2013-014, Indira Gandhi Institute of Development Research, Mumbai, India.

    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:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2837-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.