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

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  • 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
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    3. 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.
    4. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
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