Long Jianjun, Zheng Songyin
School of Management Science and Engineering, Chongqing Technology and Business University, Chongqing, China.
PLoS One. 2025 Jul 28;20(7):e0328071. doi: 10.1371/journal.pone.0328071. eCollection 2025.
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.
有限理性、信息不对称、研发溢出等现象是经济系统中普遍存在的特征，但在有限理性框架内同时研究研发溢出和信息不对称的文献仍然较少。本研究创新性地将单向研发溢出、有效信息和政府研发补贴纳入动态两阶段Stackelberg - Bertrand模型。通过应用 Jury 准则，系统分析了所有均衡点的稳定性特征，推导了稳定性条件和稳定区域，并研究了该离散系统的复杂动力学。主要研究结果表明：（1）研发领导者有效信息的增强和政府研发补贴的增加对均衡价格具有稳定作用；（2）产品过度同质化可能导致价格大幅波动或混沌动态，而更大的产品差异化则提高了领导者的盈利能力；（3）适度的研发溢出有助于价格稳定，虽然部分降低了领先企业的利润，但为企业集群发展产生了正外部性。本研究为寡头垄断市场中的创新策略和差异化产品开发提供了重要的理论见解和实践启示。
