IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v143y2016icp9-12.html
   My bibliography  Save this article

On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation

Author

Listed:
  • Lambertini, Luca
  • Mantovani, Andrea

Abstract

We revisit Fujiwara’s (2008) linear–quadratic differential duopoly game to show that the degenerate nonlinear feedback identified by the tangency point with the stationary state line is indeed unstable, given the dynamics of the natural resource exploited by firms. To do so, we fully characterise the continuum of nonlinear feedback solution via Rowat’s (2007) method, thereby identifying the infinitely many stable nonlinear feedback equilibria. This entails that Rowat’s method can be used in games where each player’s instantaneous payoff depends quadratically on all players’ controls.

Suggested Citation

  • Lambertini, Luca & Mantovani, Andrea, 2016. "On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation," Economics Letters, Elsevier, vol. 143(C), pages 9-12.
    • Handle: RePEc:eee:ecolet:v:143:y:2016:i:c:p:9-12
    DOI: 10.1016/j.econlet.2016.03.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176516300878
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2016.03.015?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    2. Rubio, Santiago J. & Casino, Begona, 2002. "A note on cooperative versus non-cooperative strategies in international pollution control," Resource and Energy Economics, Elsevier, vol. 24(3), pages 251-261, June.
    3. Itaya, Jun-ichi & Shimomura, Koji, 2001. "A dynamic conjectural variations model in the private provision of public goods: a differential game approach," Journal of Public Economics, Elsevier, vol. 81(1), pages 153-172, July.
    4. Benchekroun, Hassan, 2003. "Unilateral production restrictions in a dynamic duopoly," Journal of Economic Theory, Elsevier, vol. 111(2), pages 214-239, August.
    5. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
    6. Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October.
    7. Colombo, Luca & Labrecciosa, Paola, 2015. "On the Markovian efficiency of Bertrand and Cournot equilibria," Journal of Economic Theory, Elsevier, vol. 155(C), pages 332-358.
    8. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, November.
    9. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
    10. Benchekroun, Hassan, 2008. "Comparative dynamics in a productive asset oligopoly," Journal of Economic Theory, Elsevier, vol. 138(1), pages 237-261, January.
    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. Benchekroun, Hassan & Ray Chaudhuri, Amrita & Tasneem, Dina, 2020. "On the impact of trade in a common property renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 101(C).
    2. Michele Bisceglia, 2020. "Optimal taxation in a common resource oligopoly game," Journal of Economics, Springer, vol. 129(1), pages 1-31, January.
    3. Santiago Rendon-Marin & Luis Felipe Higuita-Gutiérrez & Diana Maryory Gomez-Gallego, 2024. "Knowledge, Attitudes, and Practices Regarding Air Pollution among Medical Students," IJERPH, MDPI, vol. 21(6), pages 1-15, June.
    4. Yuankan Huang & Takehiro Inohara, 2023. "Stable Markov perfect equilibria in the asymmetric differential-game duopoly with a renewable resource," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 45-63, April.
    5. Lambertini, Luca, 2021. "Regulating the tragedy of commons: Nonlinear feedback solutions of a differential game with a dual interpretation," Energy Economics, Elsevier, vol. 100(C).
    6. Luca Lambertini & Arsen Palestini, 2018. "Voluntary Export Restraints in a Trade Model with Sticky Price: Linear and Nonlinear Feedback Solutions," Dynamic Games and Applications, Springer, vol. 8(3), pages 507-518, September.
    7. L. Lambertini & G. Leitmann, 2017. "On the attainment of the maximum sustainable yield in the Verhulst-Lotka-Volterra model," Working Papers wp1112, Dipartimento Scienze Economiche, Universita' di Bologna.
    8. Feichtinger, Gustav & Lambertini, Luca & Leitmann, George & Wrzaczek, Stefan, 2022. "Managing the tragedy of commons and polluting emissions: A unified view," European Journal of Operational Research, Elsevier, vol. 303(1), pages 487-499.
    9. N. Baris Vardar & Georges Zaccour, 2020. "Exploitation of a Productive Asset in the Presence of Strategic Behavior and Pollution Externalities," Mathematics, MDPI, vol. 8(10), pages 1-28, October.

    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. Lambertini, Luca, 2021. "Regulating the tragedy of commons: Nonlinear feedback solutions of a differential game with a dual interpretation," Energy Economics, Elsevier, vol. 100(C).
    2. Luca Lambertini, 2016. "Managerial Delegation in a Dynamic Renewable Resource Oligopoly," Dynamic Modeling and Econometrics in Economics and Finance, in: Herbert Dawid & Karl F. Doerner & Gustav Feichtinger & Peter M. Kort & Andrea Seidl (ed.), Dynamic Perspectives on Managerial Decision Making, pages 93-107, Springer.
    3. Tasneem, Dina & Engle-Warnick, Jim & Benchekroun, Hassan, 2017. "An experimental study of a common property renewable resource game in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 91-119.
    4. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    5. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    6. Luca Grilli & Michele Bisceglia, 2020. "A dynamic private property resource game with asymmetric firms," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 109-127, June.
    7. Feichtinger, Gustav & Lambertini, Luca & Leitmann, George & Wrzaczek, Stefan, 2022. "Managing the tragedy of commons and polluting emissions: A unified view," European Journal of Operational Research, Elsevier, vol. 303(1), pages 487-499.
    8. Michele Bisceglia, 2020. "Optimal taxation in a common resource oligopoly game," Journal of Economics, Springer, vol. 129(1), pages 1-31, January.
    9. Luca Grilli & Michele Bisceglia, 2017. "A Duopoly with Common Renewable Resource and Incentives," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-20, December.
    10. Luca Grilli & Michele Bisceglia, 2017. "A differential game in a duopoly with instantaneous incentives," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 317-333, November.
    11. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
    12. Benchekroun, Hassan & Ray Chaudhuri, Amrita & Tasneem, Dina, 2020. "On the impact of trade in a common property renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 101(C).
    13. Javier Frutos & Guiomar Martín-Herrán, 2018. "Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games," Dynamic Games and Applications, Springer, vol. 8(3), pages 620-636, September.
    14. N. Baris Vardar & Georges Zaccour, 2020. "Exploitation of a Productive Asset in the Presence of Strategic Behavior and Pollution Externalities," Mathematics, MDPI, vol. 8(10), pages 1-28, October.
    15. Benchekroun, Hassan & Long, Ngo Van, 2016. "Status concern and the exploitation of common pool renewable resources," Ecological Economics, Elsevier, vol. 125(C), pages 70-82.
    16. Colombo, Luca & Labrecciosa, Paola, 2022. "Product quality differentiation in a renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 111(C).
    17. Eggert, Wolfgang & Itaya, Jun-ichi & Mino, Kazuo, 2011. "A dynamic model of conflict and appropriation," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 167-182.
    18. Colombo, Luca & Labrecciosa, Paola, 2019. "Stackelberg versus Cournot: A differential game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 239-261.
    19. Colombo, Luca & Labrecciosa, Paola, 2018. "Consumer surplus-enhancing cooperation in a natural resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 92(C), pages 185-193.
    20. Fujiwara, Kenji, 2011. "Losses from competition in a dynamic game model of a renewable resource oligopoly," Resource and Energy Economics, Elsevier, vol. 33(1), pages 1-11, January.

    More about this item

    Keywords

    Differential games; Renewable resources; Feedback strategies;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • Q2 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation

    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:ecolet:v:143:y:2016:i:c:p:9-12. 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/ecolet .

    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.