收益模糊与混合更新产业集群合作演化博弈

Uncertainty and Hybrid Update in the Evolutionary Game of Industrial Cluster Cooperation

摘要: 针对产业集群合作创新中收益不确定性与企业行为模式异质性并存的问题，采用三角模糊数刻画收益不确定性，基于雪堆博弈设定支付矩阵，在正则网络上引入混合更新机制(模仿更新IM、死亡–出生DB、出生–死亡BD按比例并存)，通过重心法去模糊化，建立弱选择下的复制动态方程并进行蒙特卡洛仿真。结果表明：混合更新机制可通过调节IM权重连续调控合作水平，纯IM促进合作能力最强，纯BD最弱；网络密度对合作呈倒U型影响；不同拓扑下合作水平差异显著，随机图最高，小世界最差，无标度网络因枢纽节点两极分化而波动剧烈。理论分析给出合作演化的方向性判据，有限种群仿真中合作水平在中间值波动，二者相互补充。产业集群治理应优先引导模仿学习文化，构建适度连接的网络结构，针对不同拓扑采取差异化策略。研究为不确定环境下合作演化提供了运筹分析框架。

Abstract: In response to the problem of the coexistence of uncertainty in returns and heterogeneity in enterprise behavior patterns in industrial cluster cooperative innovation, triangular fuzzy numbers are used to depict the uncertainty of returns. The payment matrix is set based on the Snowdrift Game. A hybrid update mechanism (imitative update IM, death-birth DB, birth-death BD, existing in proportion) is introduced on the regular network. The defuzzification is carried out by the center of gravity method, and the replication dynamic equation under weak selection is established and a Monte Carlo simulation is conducted. The results show that the hybrid update mechanism can continuously regulate the cooperation level by adjusting the IM weight. Pure IM promotes the cooperation ability the most, while pure BD is the weakest. Network density has an inverted U-shaped impact on cooperation. The cooperation level varies significantly under different topologies. Random graphs have the highest level, while small-world networks have the lowest. Scale-free networks fluctuate violently due to the polarization of hub nodes. The theoretical analysis provides a directional criterion for the evolution of cooperation. In the finite population simulation, the cooperation level fluctuates at the intermediate value, and the two complement each other. Cluster governance should prioritize guiding the imitation learning culture, constructing a moderately connected network structure, and adopting differentiated strategies for different topologies. The research provides an operational analysis framework for cooperative evolution in uncertain environments.