IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v93y2016icp151-161.html
   My bibliography  Save this article

Complex dynamics and multistability with increasing rationality in market games

Author

Listed:
  • Cavalli, Fausto
  • Naimzada, Ahmad

Abstract

In this work we study oligopoly models in which firms adopt decision mechanisms based on best response techniques with different rationality degrees. Firms are also assumed to face resource or financial constraints in adjusting their production levels, so that, from time to time, they can only increase or decrease their strategy by a bounded quantity. We consider different families of oligopolies of generic sizes, characterized by heterogeneous compositions with respect to the rationality degrees of firms. We analytically study the local stability of the equilibrium depending on the oligopoly size and composition and through numerical simulations we investigate the possible dynamics arising when trajectories do not converge toward the equilibrium. We show that in this case complex dynamics can arise, and this is due to both the loss of stability of the equilibrium and to the emergence of multiple attractors, with the stable steady state coexisting with a different, periodic or chaotic, attractor. In particular, we show that multistability phenomena occur when the overall degree of rationality of the oligopoly is increased. Finally, we investigate the effect of non-convergent dynamics on the realized profits.

Suggested Citation

  • Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    • Handle: RePEc:eee:chsofr:v:93:y:2016:i:c:p:151-161
    DOI: 10.1016/j.chaos.2016.10.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916303095
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.10.014?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. Akio Matsumoto & Ferenc Szidarovszky, 2011. "Stability, Bifurcation, and Chaos in N -Firm Nonlinear Cournot Games," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-22, February.
    2. Du, Jian-guo & Fan, Yue-qian & Sheng, Zhao-han & Hou, Yun-zhang, 2013. "Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter," Economic Modelling, Elsevier, vol. 33(C), pages 507-516.
    3. Droste, Edward & Hommes, Cars & Tuinstra, Jan, 2002. "Endogenous fluctuations under evolutionary pressure in Cournot competition," Games and Economic Behavior, Elsevier, vol. 40(2), pages 232-269, August.
    4. 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.
    5. Naimzada, Ahmad & Ricchiuti, Giorgio, 2011. "Monopoly with local knowledge of demand function," Economic Modelling, Elsevier, vol. 28(1-2), pages 299-307, January.
    6. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    7. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    8. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    9. Lampart, Marek, 2012. "Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1081-1085.
    10. Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    11. William A. Brock & Cars H. Hommes, 2001. "A Rational Route to Randomness," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 16, pages 402-438, Edward Elgar Publishing.
    12. Cerboni Baiardi, Lorenzo & Lamantia, Fabio & Radi, Davide, 2015. "Evolutionary competition between boundedly rational behavioral rules in oligopoly games," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 204-225.
    13. Naimzada, Ahmad K. & Tramontana, Fabio, 2009. "Controlling chaos through local knowledge," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2439-2449.
    14. 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.
    15. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    16. Askar, S.S. & Alnowibet, K., 2016. "Nonlinear oligopolistic game with isoelastic demand function: Rationality and local monopolistic approximation," Chaos, Solitons & Fractals, Elsevier, vol. 84(C), pages 15-22.
    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. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    2. Fausto Cavalli & Ahmad Naimzada & Nicol`o Pecora & Marina Pireddu, 2018. "Agents' beliefs and economic regimes polarization in interacting markets," Papers 1805.00387, arXiv.org.
    3. Fang Wu & Junhai Ma, 2023. "Research Trend, Logical Structure and Outlook on Complex Economic Game," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    4. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. 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).
    6. Oleg Bazaluk & Svitlana Balinchenko, 2020. "Dynamic Coordination of Internal Displacement: Return and Integration Cases in Ukraine and Georgia," Sustainability, MDPI, vol. 12(10), pages 1-17, May.

    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. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2018. "An evolutionary model with best response and imitative rules," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 313-333, November.
    2. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2019. "An evolutionary Cournot oligopoly model with imitators and perfect foresight best responders," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 458-475, July.
    3. 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.
    4. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2018. "An oligopoly model with best response and imitation rules," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 193-205.
    5. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    6. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2019. "An oligopoly model with rational and imitation rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 254-278.
    7. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    8. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    9. Sarah Mignot & Fabio Tramontana & Frank Westerhoff, 2024. "Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior," Annals of Operations Research, Springer, vol. 337(3), pages 809-834, June.
    10. Anufriev, Mikhail & Kopányi, Dávid, 2018. "Oligopoly game: Price makers meet price takers," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 84-103.
    11. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    12. Domenico De Giovanni & Fabio Lamantia, 2016. "Control delegation, information and beliefs in evolutionary oligopolies," Journal of Evolutionary Economics, Springer, vol. 26(5), pages 1089-1116, December.
    13. Lamantia, Fabio & Pezzino, Mario, 2016. "Evolutionary efficacy of a Pay for Performance scheme with motivated agents," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 107-119.
    14. 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.
    15. Schmitt, Noemi & Tuinstra, Jan & Westerhoff, Frank, 2017. "Side effects of nonlinear profit taxes in an evolutionary market entry model: Abrupt changes, coexisting attractors and hysteresis problems," Journal of Economic Behavior & Organization, Elsevier, vol. 135(C), pages 15-38.
    16. Luca Gori & Luca Guerrini & Mauro Sodini, 2014. "Hopf Bifurcation in a Cobweb Model with Discrete Time Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, June.
    17. 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.
    18. Domenico De Giovanni & Fabio Lamantia, 2017. "Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 877-903, November.
    19. Hommes, C.H. & Ochea, M. & Tuinstra, J., 2011. "On the stability of the Cournot equilibrium: An evolutionary approach," CeNDEF Working Papers 11-10, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    20. Davide Radi, 2017. "Walrasian versus Cournot behavior in an oligopoly of boundedly rational firms," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 933-961, November.

    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:chsofr:v:93:y:2016:i:c:p:151-161. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.