IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/62300.html
   My bibliography  Save this paper

A continuous time Cournot duopoly with delays

Author

Listed:
  • Gori, Luca
  • Guerrini, Luca
  • Sodini, Mauro

Abstract

This paper extends the classical repeated duopoly model with quantity-setting firms of Bischi et al. (1998) by assuming that production of goods is subject to some gestation lags but exchanges take place continuously on the market. The model is expressed in the form of differential equations with discrete delays. By using some recent mathematical techniques and numerical experiments, results show some dynamic phenomena that cannot be observed when delays are absent. In addition, depending on the extent of time delays and inertia, synchronisation failure can arise even in the event of homogeneous firms.

Suggested Citation

  • Gori, Luca & Guerrini, Luca & Sodini, Mauro, 2015. "A continuous time Cournot duopoly with delays," MPRA Paper 62300, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:62300
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/62300/1/MPRA_paper_62300.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. He, Xue-Zhong & Li, Kai, 2012. "Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 973-987.
    3. He, Xue-Zhong & Zheng, Min, 2010. "Dynamics of moving average rules in a continuous-time financial market model," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 615-634, December.
    4. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    5. Bambi, Mauro & Gori, Franco, 2014. "Unifying Time-To-Build Theory," Macroeconomic Dynamics, Cambridge University Press, vol. 18(8), pages 1713-1725, December.
    6. A. Krawiec & M. Szydlowski, 1999. "The Kaldor‐Kalecki business cycle model," Annals of Operations Research, Springer, vol. 89(0), pages 89-100, January.
    7. Matsumoto, Akio & Szidarovszky, Ferenc, 2012. "Nonlinear delay monopoly with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 507-519.
    8. Luca Guerrini & Mauro Sodini, 2013. "Dynamic Properties of the Solow Model with Increasing or Decreasing Population and Time-to-Build Technology," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
    9. Matsumoto, Akio & Szidarovszky, Ferenc, 2014. "Discrete and continuous dynamics in nonlinear monopolies," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 632-642.
    10. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    11. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    12. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    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. Serena Brianzoni & Giovanni Campisi & Luca Guerrini, 2018. "A continuous-time heterogeneous duopoly model with delays," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 259-275, November.
    2. Raul Villafuerte-Segura & Eduardo Alvarado-Santos & Benjamin A. Itza-Ortiz, 2019. "Conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay," Papers 1905.02817, arXiv.org, revised Oct 2019.
    3. Zhu, Yan-lan & Zhou, Wei & Chu, Tong, 2022. "Analysis of complex dynamical behavior in a mixed duopoly model with heterogeneous goods," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. Akio Matsumoto & Ferenc Szidarovszky & Keiko Nakayama, 2020. "Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    5. 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.
    6. Chen, Jianxin & Zhang, Tonghua & Zhou, Yongwu, 2020. "Dynamics of a risk-averse newsvendor model with continuous-time delay in supply chain financing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 133-148.
    7. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela, 2022. "Stability and bifurcations in a general Cournot duopoly model with distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    8. Luca Gori & Luca Guerrini & Mauro Sodini, 2017. "A characterisation of duopoly dynamics with frictions in production adjustments," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 963-988, November.

    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. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.
    2. Serena Brianzoni & Giovanni Campisi & Luca Guerrini, 2018. "A continuous-time heterogeneous duopoly model with delays," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 259-275, November.
    3. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    4. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    5. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    6. Mauro Bambi & Cristina Girolami & Salvatore Federico & Fausto Gozzi, 2017. "Generically distributed investments on flexible projects and endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 521-558, February.
    7. Krawiec, Adam & Szydłowski, Marek, 2017. "Economic growth cycles driven by investment delay," Economic Modelling, Elsevier, vol. 67(C), pages 175-183.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Akio Matsumoto & Ferenc Szidarovszky & Keiko Nakayama, 2020. "Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    14. Zsolt Bihary & Attila Andr'as V'ig, 2019. "Analytic solutions in a continuous-time financial market model," Papers 1902.09999, arXiv.org.
    15. Kamalinejad, Howra & Majd, Vahid Johari & Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2010. "Cournot games with linear regression expectations in oligopolistic markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1874-1885.
    16. He, Xue-Zhong & Li, Kai, 2012. "Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(7), pages 973-987.
    17. Luca Gori & Luca Guerrini & Mauro Sodini, 2017. "A characterisation of duopoly dynamics with frictions in production adjustments," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 963-988, November.
    18. Gian Italo Bischi & Fabio Lamantia & Davide Radi, 2018. "Evolutionary oligopoly games with heterogeneous adaptive players," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 12, pages 343-370, Edward Elgar Publishing.
    19. Georges SARAFOPOULOS & Kosmas PAPADOPOULOS, 2017. "On A Cournot Duopoly Game With Differentiated Goods, Heterogeneous Expectations And A Cost Function Including Emission Costs," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 16(1), pages 11-22.
    20. 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.

    More about this item

    Keywords

    Chaos; Cournot duopoly; Time delays;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:62300. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.