Haiping Ren, Xianrong Hu, Yong Gan, Hong Li
Enterprises in pharmaceutical clusters face challenges of uncertain collaboration returns and complex strategy updating, which are poorly captured by traditional deterministic game models. This paper develops a fuzzy evolutionary game model on a finite structured population network. Key contributions include: (1) using triangular fuzzy numbers to characterize uncertain R&D returns; (2) proposing a probability-weighted hybrid update mechanism that unifies imitation (IM), death–birth (DB), and birth–death (BD) rules, representing firms’ integrated learning, competition, and expansion behaviors. Theoretical and numerical results show: (1) the hybrid mechanism's convergence speed lies between those of pure mechanisms and is tunable via weights, while the efficiency ranking of pure mechanisms follows IM > DB > BD; (2) network degree and cooperation exhibit an inverted U-shaped relationship with an optimum; (3) greater payoff fuzziness widens the distribution range of steady-state cooperation levels and increases evolutionary uncertainty; (4) adjusting update weights—shaping cluster culture—can be a cost-effective policy lever, though the advantage over traditional subsidies depends on cost assumptions and should be interpreted as model-based implications rather than definitive policy conclusions; (5) robustness checks across network topologies show that the IM > DB > BD ranking persists in small-world networks but weakens in scale-free networks due to hub-induced uncertainty; the inverted U-shaped relationship holds for regular and small-world networks but vanishes in scale-free networks. This study advances fuzzy-fitness evolutionary game theory and provides a quantitative framework for enhancing cluster collaboration through network optimization, uncertainty management, and cultural guidance.