IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p489-d507009.html
   My bibliography  Save this article

A Dynamic Model of Cournot Competition for an Oligopolistic Market

Author

Listed:
  • Zeng Lian

    (International Business School, Beijing Foreign Studies University, Beijing 100089, China)

  • Jie Zheng

    (Department of Economics, School of Economics and Management, Tsinghua University, Beijing 100084, China)

Abstract

This paper studies firms’ dynamic interaction in a Cournot market. In each period of the game, the firm decides whether to make a stochastic positioning investment (establishing or maintaining its position in market competition). The market demand is also stochastic (high or low). By adopting symmetric Market perfect Nash equilibrium, firms choose strategies to maximize the discounted present value of cash flow. By considering the cases with one, two, and three active firms in the market, respectively, we present the stage game market outcome, show the transition probabilities, find the steady state of the system, and discuss the speed of convergence. Our work allows for two types of uncertainty in firms’ interactions, which contribute to the dynamic oligopoly literature.

Suggested Citation

  • Zeng Lian & Jie Zheng, 2021. "A Dynamic Model of Cournot Competition for an Oligopolistic Market," Mathematics, MDPI, vol. 9(5), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:489-:d:507009
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/489/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/489/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. E. Caves & M. E. Porter, 1977. "From Entry Barriers to Mobility Barriers: Conjectural Decisions and Contrived Deterrence to New Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(2), pages 241-261.
    2. A. Michael Spence, 1979. "Investment Strategy and Growth in a New Market," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 1-19, Spring.
    3. 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.
    4. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, December.
    5. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    6. Gilbert, Richard & Harris, Richard G., 1984. "Competition with Lumpy Investment," Department of Economics, Working Paper Series qt11v5q20z, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    7. Dixit, Avinash, 1980. "The Role of Investment in Entry-Deterrence," Economic Journal, Royal Economic Society, vol. 90(357), pages 95-106, March.
    8. Piga, Claudio A. G., 2000. "Competition in a duopoly with sticky price and advertising," International Journal of Industrial Organization, Elsevier, vol. 18(4), pages 595-614, May.
    9. Fudenberg, Drew & Tirole, Jean, 1984. "The Fat-Cat Effect, the Puppy-Dog Ploy, and the Lean and Hungry Look," American Economic Review, American Economic Association, vol. 74(2), pages 361-366, May.
    10. Richard J. Gilbert & Richard G. Harris, 1984. "Competition with Lumpy Investment," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 197-212, Summer.
    11. Salop, Steven C, 1979. "Strategic Entry Deterrence," American Economic Review, American Economic Association, vol. 69(2), pages 335-338, May.
    12. Brito, Duarte, 2003. "Preemptive mergers under spatial competition," International Journal of Industrial Organization, Elsevier, vol. 21(10), pages 1601-1622, December.
    13. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-569, May.
    14. Bhattacharya, Mita & Bloch, Harry, 2000. "The dynamics of industrial concentration in Australian manufacturing," International Journal of Industrial Organization, Elsevier, vol. 18(8), pages 1181-1199, December.
    15. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    16. B. Curtis Eaton & Richard G. Lipsey, 1980. "Exit Barriers are Entry Barriers: The Durability of Capital as a Barrier to Entry," Bell Journal of Economics, The RAND Corporation, vol. 11(2), pages 721-729, Autumn.
    17. Eaton, B Curtis & Lipsey, Richard G, 1978. "Freedom of Entry and the Existence of Pure Profit," Economic Journal, Royal Economic Society, vol. 88(351), pages 455-469, September.
    18. A. Michael Spence, 1977. "Entry, Capacity, Investment and Oligopolistic Pricing," Bell Journal of Economics, The RAND Corporation, vol. 8(2), pages 534-544, Autumn.
    19. Douglas S. West, 1981. "Testing for Market Preemption Using Sequential Location Data," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 129-143, Spring.
    20. 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.
    21. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    22. Kuang, Zhonghong & Lian, Zeng & Lien, Jaimie W. & Zheng, Jie, 2020. "Serial and parallel duopoly competition in multi-segment transportation routes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    23. repec:bla:econom:v:46:y:1979:i:182:p:149-58 is not listed on IDEAS
    24. V. V. Mazalov & A. V. Melnik, 2016. "Equilibrium Prices and Flows in the Passenger Traffic Problem," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-19, March.
    25. Raymond Deneckere & Carl Davidson, 1985. "Incentives to Form Coalitions with Bertrand Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 473-486, Winter.
    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. Ding, Shasha & Sun, Hao & Sun, Panfei & Han, Weibin, 2022. "Dynamic outcome of coopetition duopoly with implicit collusion," Chaos, Solitons & Fractals, Elsevier, vol. 160(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. repec:clg:wpaper:2013-26 is not listed on IDEAS
    2. Harry Bloch & Curtis Eaton & Robert Rothschild, 2013. "Does market size matter?," Working Papers 35024217, Lancaster University Management School, Economics Department.
    3. Harry Bloch & B. Curtis Eaton & R. Rothschild, 2014. "A Dynamic Model of Oligopolistic Market Structure, Featuring Positioning Investments," International Journal of the Economics of Business, Taylor & Francis Journals, vol. 21(3), pages 379-411, November.
    4. Bergman, Mats A., 1998. "Endogenous Timing of Investments Yields Modified Stackelberg Outcomes," SSE/EFI Working Paper Series in Economics and Finance 272, Stockholm School of Economics.
    5. Drew Fudenberg, 2015. "Tirole's Industrial Regulation and Organization Legacy in Economics," Scandinavian Journal of Economics, Wiley Blackwell, vol. 117(3), pages 771-800, July.
    6. Michael Waldman, 1983. "Limited Collusion and Entry Deterence," UCLA Economics Working Papers 306, UCLA Department of Economics.
    7. Michael Waldman, 1987. "Noncooperative Entry Deterrence, Uncertainty, and the Free Rider Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 301-310.
    8. Rupayan Pal & Vinay Ramani, 2017. "Will a matchmaker invite her potential rival in?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(4), pages 806-819, December.
    9. Barrie R. Nault & Mark B. Vandenbosch, 2000. "Research Report: Disruptive Technologies—Explaining Entry in Next Generation Information Technology Markets," Information Systems Research, INFORMS, vol. 11(3), pages 304-319, September.
    10. Kyle Bagwell & Garey Ramey, 1996. "Capacity, Entry, and Forward Induction," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 660-680, Winter.
    11. Sorgard, Lars, 1997. "Judo economics reconsidered: Capacity limitation, entry and collusion," International Journal of Industrial Organization, Elsevier, vol. 15(3), pages 349-368, May.
    12. Committee, Nobel Prize, 2014. "Market power and regulation (scientific background)," Nobel Prize in Economics documents 2014-2, Nobel Prize Committee.
    13. Xavier Martinez-Giralt & Barros Pedro Pita, 2005. "Bargaining and idle public sector capacity in health care," Economics Bulletin, AccessEcon, vol. 9(5), pages 1-8.
    14. Michael Waldman, 1987. "Underinvestment in Entry Deterrence: When and Why," UCLA Economics Working Papers 456, UCLA Department of Economics.
    15. Pedro Barros & Xavier Martinez-Giralt, 2005. "Negotiation Advantages of Professional Associations in Health Care," International Journal of Health Economics and Management, Springer, vol. 5(2), pages 191-204, June.
    16. Dennis W. Carlton & Michael Waldman, 2002. "The Strategic Use of Tying to Preserve and Create Market Power in Evolving Industries," RAND Journal of Economics, The RAND Corporation, vol. 33(2), pages 194-220, Summer.
    17. Miettinen, Topi & Perea, Andrés, 2015. "Commitment in alternating offers bargaining," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 12-18.
    18. Barbara J. Spencer & James A. Brander, 1983. "International R & D Rivalry and Industrial Strategy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 707-722.
    19. Jensen, Richard & Showalter, Dean, 2004. "Strategic debt and patent races," International Journal of Industrial Organization, Elsevier, vol. 22(7), pages 887-915, September.
    20. Jean-Pierre Ponssard, 2004. "Rent Dissipation in Repeated Entry Games: Some New Results," CESifo Working Paper Series 1186, CESifo.
    21. Vernasca, Gianluigi, 2003. "Dynamic Price Competition With Price Adjustment Costs And Product Differentiation," The Warwick Economics Research Paper Series (TWERPS) 681, University of Warwick, Department of Economics.

    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:gam:jmathe:v:9:y:2021:i:5:p:489-:d:507009. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.