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<p>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&amp;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 &gt; DB &gt; 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 &gt; DB &gt; 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.</p>

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Evolutionary game analysis of pharmaceutical industry cluster cooperation with fuzzy payoffs and hybrid updating

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年8月1日

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  • Haiping Ren,
  • Xianrong Hu,
  • Yueyang Gan,
  • Hong Li

摘要

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.