IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v79y2015icp178-190.html
   My bibliography  Save this article

A nonlinear Cournot duopoly with advertising

Author

Listed:
  • Gori, Luca
  • Sodini, Mauro
  • Fanti, Luciano

Abstract

This paper aims at studying local and global dynamics in a nonlinear duopoly with quantity-setting firms and non-cooperative advertising investments that affect the degree of (horizontally) differentiated products. It concentrates on persuasive advertising in a model where each firm has limited information and uses a behavioural rule to set the quantity for the subsequent period. By using some mathematical techniques and numerical simulations, our results show the existence of weak (à la Milnor) attractors, multistability and chaotic dynamics. In the long term, firms may continuously shift from states in which they invest in advertising to states in which advertising investment is absent.

Suggested Citation

  • Gori, Luca & Sodini, Mauro & Fanti, Luciano, 2015. "A nonlinear Cournot duopoly with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 178-190.
    • Handle: RePEc:eee:chsofr:v:79:y:2015:i:c:p:178-190
    DOI: 10.1016/j.chaos.2015.01.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915000296
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.01.022?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. Radi, Davide & Gardini, Laura & Avrutin, Viktor, 2014. "The role of constraints in a segregation model: The symmetric case," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 103-119.
    2. Hamilton, Stephen F., 2009. "Informative advertising in differentiated oligopoly markets," International Journal of Industrial Organization, Elsevier, vol. 27(1), pages 60-69, January.
    3. Fershtman, Chaim & Gandal, Neil, 1994. "Disadvantageous semicollusion," International Journal of Industrial Organization, Elsevier, vol. 12(2), pages 141-154, June.
    4. Stahl II Dale O., 1994. "Oligopolistic Pricing and Advertising," Journal of Economic Theory, Elsevier, vol. 64(1), pages 162-177, October.
    5. 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.
    6. Michael Kopel & Luca Lambertini, 2013. "On Price Competition with Market Share Delegation Contracts," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 34(1), pages 40-43, January.
    7. 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.
    8. Luciano Fanti & Luca Gori & Mauro Sodini, 2013. "Nonlinear Dynamics in a Cournot Duopoly with Different Attitudes towards Strategic Uncertainty," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, December.
    9. Gene M. Grossman & Carl Shapiro, 1984. "Informative Advertising with Differentiated Products," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(1), pages 63-81.
    10. Avinash Dixit & Victor Norman, 1978. "Advertising and Welfare," Bell Journal of Economics, The RAND Corporation, vol. 9(1), pages 1-17, Spring.
    11. 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.
    12. Brod, Andrew & Shivakumar, Ram, 1999. "Advantageous Semi-collusion," Journal of Industrial Economics, Wiley Blackwell, vol. 47(2), pages 221-230, June.
    13. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
    14. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    15. Bagwell, Kyle, 2007. "The Economic Analysis of Advertising," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 28, pages 1701-1844, Elsevier.
    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. Luca Gori & Nicolò Pecora & Mauro Sodini, 2017. "Market share delegation in a nonlinear duopoly with quantity competition: the role of dynamic entry barriers," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 905-931, November.
    2. Malcolm Brady, 2021. "A Game-Theoretic Model of Strategic Interaction Using Advertising: Simulating the Evolution of the Cournot Nash Equilibrium under Different Competitive Scenarios," Games, MDPI, vol. 12(4), pages 1-16, November.
    3. Malcolm Brady, 2022. "Asymmetric Horizontal Differentiation under Advertising in a Cournot Duopoly," Games, MDPI, vol. 13(3), pages 1-14, May.
    4. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(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. 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.
    2. Wang, Shinn-Shyr & Stiegert, Kyle W., 2006. "The Duopolistic Firm with Endogenous Risk Control: Case of Persuasive Advertising and Product Differentiation," Staff Paper Series 496, University of Wisconsin, Agricultural and Applied Economics.
    3. Zhang, Jianqiang & Cao, Qingning & He, Xiuli, 2020. "Manufacturer encroachment with advertising," Omega, Elsevier, vol. 91(C).
    4. 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.
    5. Simon P. Anderson & Régis Renault, 2006. "Advertising Content," American Economic Review, American Economic Association, vol. 96(1), pages 93-113, March.
    6. Astorne-Figari, Carmen & López, José Joaquín & Yankelevich, Aleksandr, 2019. "Advertising for consideration," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 653-669.
    7. Ivan Pastine & Tuvana Pastine, 2011. "Coordination In Markets With Consumption Externalities: Advertising And Product Quality," Manchester School, University of Manchester, vol. 79(1), pages 45-62, January.
    8. Brianzoni, Serena & Gori, Luca & Michetti, Elisabetta, 2015. "Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 191-203.
    9. Simon P. Anderson & André De Palma, 2009. "Information congestion," RAND Journal of Economics, RAND Corporation, vol. 40(4), pages 688-709, December.
    10. Christou, C. & Vettas, N., 2008. "On informative advertising and product differentiation," International Journal of Industrial Organization, Elsevier, vol. 26(1), pages 92-112, January.
    11. Creane, Anthony & Manduchi, Agostino, 2022. "Informative advertising in monopolistically competitive markets," International Journal of Industrial Organization, Elsevier, vol. 83(C).
    12. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899, January.
    13. Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    14. Jianqiang Zhang & Weijun Zhong & Shue Mei, 2012. "Competitive effects of informative advertising in distribution channels," Marketing Letters, Springer, vol. 23(3), pages 561-584, September.
    15. Simon P. Anderson & André de Palma, 2012. "Competition for attention in the Information (overload) Age," RAND Journal of Economics, RAND Corporation, vol. 43(1), pages 1-25, March.
    16. Alejandro Corvalán & Pablo Serra, 2005. "Sunk Prices And Salesforce Competition," Documentos de Trabajo 216, Centro de Economía Aplicada, Universidad de Chile.
    17. Laurent Cavenaile & Pau Roldan-Blanco, 2021. "Advertising, Innovation, and Economic Growth," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 251-303, July.
    18. Lola Esteban & José M. Hernández & José Luis Moraga‐González, 2006. "Customer Directed Advertising and Product Quality," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(4), pages 943-968, December.
    19. Salvatore Piccolo & Piero Tedeschi & Giovanni Ursino, 2018. "Deceptive Advertising with Rational Buyers," Management Science, INFORMS, vol. 64(3), pages 1291-1310, March.
    20. Massimo Motta, 2013. "Advertising bans," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(1), pages 61-81, March.

    More about this item

    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:chsofr:v:79:y:2015:i:c:p:178-190. 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.