IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0328071.html

Dynamic complexity of Stackelberg-Bertrand game with one-way R&D spillovers, effective information and government subsidies

Author

Listed:
  • Jianjun Long
  • Songyin Zheng

Abstract

The phenomena of bounded rationality, asymmetric information, research and development (R&D) spillovers represent ubiquitous characteristics in economic systems, yet research simultaneously investigating R&D spillovers and information asymmetry within a bounded rationality framework remains scarce. This study innovatively incorporates one-way R&D spillovers, effective information, and government R&D subsidies into a dynamical two-stage Stackelberg-Bertrand model. Through application of Jury criterion, we systematically analyze the stability characteristics of all equilibrium points, derive stability conditions and stable regions, and investigate the complex dynamics of this discrete system. The principal findings reveal that: (1) Enhanced effective information for the R&D leader and increased government R&D subsidies exhibit stabilizing effects on equilibrium prices; (2) Excessive product homogeneity may induce substantial price volatility or chaotic dynamics, whereas greater product differentiation enhances profitability for the leader; (3) Moderate levels of R&D spillovers contribute to price stabilization, and while partially reducing leading firms’ profits, they generate positive externalities for enterprise cluster development. This research provides significant theoretical insights and practical implications for innovation strategies and differentiated product development in oligopolistic markets.

Suggested Citation

  • Jianjun Long & Songyin Zheng, 2025. "Dynamic complexity of Stackelberg-Bertrand game with one-way R&D spillovers, effective information and government subsidies," PLOS ONE, Public Library of Science, vol. 20(7), pages 1-26, July.
    • Handle: RePEc:plo:pone00:0328071
    DOI: 10.1371/journal.pone.0328071
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0328071
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0328071&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0328071?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
    ---><---

    References listed on IDEAS

    as
    1. d'Aspremont, Claude & Jacquemin, Alexis, 1990. "Cooperative and Noncooperative R&D in Duopoly with Spillovers: Erratum," American Economic Review, American Economic Association, vol. 80(3), pages 641-642, June.
    2. Maryann Feldman, 1999. "The New Economics Of Innovation, Spillovers And Agglomeration: Areview Of Empirical Studies," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 8(1-2), pages 5-25.
    3. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    Full references (including those not matched with items on IDEAS)

    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. Long, Jianjun & Wang, Fenglian, 2024. "Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 606-621.
    2. Thomas Doring & Jan Schnellenbach, 2006. "What do we know about geographical knowledge spillovers and regional growth?: A survey of the literature," Regional Studies, Taylor & Francis Journals, vol. 40(3), pages 375-395.
    3. Kraft, Kornelius & Rammer, Christian, 2023. "Intended and unintended knowledge spillovers in innovation," ZEW Discussion Papers 23-015, ZEW - Leibniz Centre for European Economic Research.
    4. Rajeev K. Goel, 2023. "Seek foreign funds or technology? Relative impacts of different spillover modes on innovation," The Journal of Technology Transfer, Springer, vol. 48(4), pages 1466-1488, August.
    5. Kaiser, Ulrich, 2002. "Measuring knowledge spillovers in manufacturing and services: an empirical assessment of alternative approaches," Research Policy, Elsevier, vol. 31(1), pages 125-144, January.
    6. Grunfeld, Leo A., 2003. "Meet me halfway but don't rush: absorptive capacity and strategic R&D investment revisited," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1091-1109, October.
    7. Prokop, Jacek & Karbowski, Adam, 2013. "R&D cooperation and industry cartelization," Economics Discussion Papers 2013-41, Kiel Institute for the World Economy.
    8. Frey, Rainer & Hussinger, Katrin, 2006. "The role of technology in M&As: a firm-level comparison of cross-border and domestic deals," Discussion Paper Series 1: Economic Studies 2006,45, Deutsche Bundesbank.
    9. Levy, Nadav, 2012. "Technology sharing and tacit collusion," International Journal of Industrial Organization, Elsevier, vol. 30(2), pages 204-216.
    10. Isaksson, Olov H.D. & Simeth, Markus & Seifert, Ralf W., 2016. "Knowledge spillovers in the supply chain: Evidence from the high tech sectors," Research Policy, Elsevier, vol. 45(3), pages 699-706.
    11. Colombo, Massimo G. & Garrone, Paola, 1998. "Common carriers' entry into multimedia services," Information Economics and Policy, Elsevier, vol. 10(1), pages 77-105, March.
    12. Haraguchi, Junichi & Matsumura, Toshihiro, 2017. "Firms' Costs, Profits, Entries, and Innovation under Optimal Privatization Policy," MPRA Paper 80927, University Library of Munich, Germany.
    13. Vasileios Zikos, 2010. "R&D Collaboration Networks in Mixed Oligopoly," Southern Economic Journal, John Wiley & Sons, vol. 77(1), pages 189-212, July.
    14. Karbowski, Adam & Prokop, Jacek, 2019. "The Impact of Vertical R&D Cooperation on Market Performance of Firms," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 7(4), pages 73-89.
    15. Agrawal, Ajay & Cockburn, Iain, 2003. "The anchor tenant hypothesis: exploring the role of large, local, R&D-intensive firms in regional innovation systems," International Journal of Industrial Organization, Elsevier, vol. 21(9), pages 1227-1253, November.
    16. Julia Müller & Thorsten Upmann, 2026. "Returns to Scale and Strategic Regimes in Innovation Races," CESifo Working Paper Series 12552, CESifo.
    17. Muhamed Kudic & Wilfried Ehrenfeld & Toralf Pusch, 2015. "On the trail of core–periphery patterns in innovation networks: measurements and new empirical findings from the German laser industry," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 55(1), pages 187-220, October.
    18. Flavio M. Menezes & Jorge Pereira, 2026. "Imperfect Competition, Emissions Tax and the Porter Hypothesis," World Scientific Book Chapters, in: Joanna Poyago-Theotoky (ed.), Green Innovation and Industrial Organization, chapter 3, pages 51-76, World Scientific Publishing Co. Pte. Ltd..
    19. Martin Andersson & Börje Johansson, 2008. "Innovation Ideas and Regional Characteristics: Product Innovations and Export Entrepreneurship by Firms in Swedish Regions," Growth and Change, Wiley Blackwell, vol. 39(2), pages 193-224, June.
    20. Buccella, Domenico & Fanti, Luciano & Gori, Luca, 2021. "A contribution to the theory of R&D investments," GLO Discussion Paper Series 940, Global Labor Organization (GLO).

    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:plo:pone00:0328071. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.