第5期 武利琴，等：基于半张量积的企业创新网络演化博弈 ·781· 建立企业创新双层耦合网络。运用矩阵半张量积 IUR evolutionary game model on the patent cooperate of 方法，以“智猪博弈”为基本博弈，得到每一时刻各 Shandong China[J].Physic A:statistical mechanics and its 企业的策略，整个网络局势演化随时间改变；根 applications,2017,475:11-23. 据收益函数得到整个网络的最优稳定纳什均衡 [10]CHENG Daizhan,XU Tingting,QI Hongsheng.Evolu- 点；最后，通过政府调控，改变博弈的基本矩阵， tionary stability strategy of networked evolutionary 从而达到最优稳定纳什均衡状态，即所有企业全 games[J].IEEE transactions on neural networks and 部创新。 learning systems,,2014,25(7):1335-1345. 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[20]ZHAO Guodong,WANG Yuzhen.Formulation and op- WANG Jian,ZHAO Kai.Cooperative innovation of enter- timization control of a class of networked evolutionary prises under "Boxed pig Game"-a research based on games with switched topologies[J].Nonlinear analysis: asymmetric evolutionary game[J].Science and technology hybrid systems,2016,22:98-107. and economy,.2016,292:21-25. [21]ZHU Bing,XIA Xiaohua,WU Zhou.Evolutionary game [9]LIU Mengmeng,MA Yinghong,LIU Zhiyuan,et al.An theoretic demand-side management and control for a class建立企业创新双层耦合网络。运用矩阵半张量积 方法，以“智猪博弈”为基本博弈, 得到每一时刻各 企业的策略，整个网络局势演化随时间改变； 根 据收益函数得到整个网络的最优稳定纳什均衡 点； 最后，通过政府调控, 改变博弈的基本矩阵， 从而达到最优稳定纳什均衡状态，即所有企业全 部创新。 参考文献： WU Qingchu, LOU Yijun, ZHU Wenfang. Epidemic out￾break for an SIS model in multiplex networks with immun￾ization[J]. Mathematical biosciences, 2016, 277: 38–46. [1] WANG Danzhu, LANG M X, SUN Yan. Evolutionary game analysis of co-opetition relationship between region￾al logistics nodes[J]. Journal of applied research and tech￾nology, 2014, 12(2): 251–260. [2] ETESAMI S R, BASAR T. Complexity of equilibrium in diffusion games on social networks[C]//Proceedings of 2014 American Control Conference. Portland, USA, 2014: 2065–2070. [3] YAN Yongyi, CHEN Zengqiang, YUE Jumei. STP ap￾proach to controlliability of finite state machines[J]. Ifac￾PapersonLine, 2015, 48(28): 138–143. [4] 于斌斌, 余雷. 基于演化博弈的集群企业创新模式选择 研究[J]. 科研管理, 2015, 36(4): 30–38. YU Binbin, YU Lei. A study on cluster enterprise techno￾logy innovation selection based on the evolutionary game[J]. Science research management, 2015, 36(4): 30–38. [5] ZHOU Qing, FANG Gang, WANG Dongpeng, et al. Re￾search on the robust optimization of the enterprise’s de￾cision on the investment to the collaborative innovation: under the risk constraints[J]. Chaos, solitons and fractals, 2016, 89: 284–289. [6] 盛光华, 张志远. 补贴方式对创新模式选择影响的演化 博弈研究[J]. 管理科学学报, 2015, 18(9): 34–45. SHENG Guanghua, ZHANG Zhiyuan. Allowance method’s influence on the innovation model choice in evolutionary game[J]. Journal of management sciences in China, 2015, 18(9): 34–45. [7] 王健, 赵凯. “智猪博弈”下的合作创新研究——基于非 对称演化博弈的分析[J]. 科技与经济, 2016, 29(2): 21–25. WANG Jian, ZHAO Kai. Cooperative innovation of enter￾prises under “Boxed pig Game”—a research based on asymmetric evolutionary game[J]. Science and technology and economy, 2016, 29(2): 21–25. [8] [9] LIU Mengmeng, MA Yinghong, LIU Zhiyuan, et al. An IUR evolutionary game model on the patent cooperate of Shandong China[J]. Physic A: statistical mechanics and its applications, 2017, 475: 11–23. CHENG Daizhan, XU Tingting, QI Hongsheng. Evolu￾tionary stability strategy of networked evolutionary games[J]. IEEE transactions on neural networks and learning systems, 2014, 25(7): 1335–1345. [10] CHENG Daizhan, HE Fenghua, QI Hongsheng, et al. Modeling, analysis and control of networked evolution￾ary games[J]. IEEE transactions on automatic control, 2015, 60(9): 2402–2415. [11] CHENG Daizhan, QI Hongsheng, HE F, et al. Semi￾tensor product approach to networked evolutionary games[J]. Control theory and technology, 2014, 12(2): 198–214. [12] CHENG Daizhan, XU Tingting, HE Fenghua, et al. On dynamics and Nash equilibriums of networked games[J]. IEEE/CAA journal of automatica sinica, 2014, 1(1): 10–18. [13] ZHAO Yin, GHOSH B K, CHENG Daizhan. Control of large-scale Boolean networks via network aggregation[J]. IEEE transactions on neural networks and learning sys￾tems, 2016, 27(7): 1527–1536. [14] LI Haitao, WANG Yuzhen, XIE Lihua. Output tracking control of Boolean control networks via state feedback: constant reference signal case[J]. Automatica, 2015, 59: 54–59. [15] LI Haitao, XIE Lihua, WANG Yuzhen. On robust control invariance of Boolean control networks[J]. Automatica, 2016, 68: 392–396. [16] CHENG Daizhan, ZHAO Yin, XU Tingting. Receding horizon based feedback optimization for mix-valued lo￾gical networks[J]. IEEE transactions on automatic control, 2015, 60(12): 3362–3366. [17] GUO Peilian, WANG Yuzhen, JIANG Ping. Nash equi￾librium, dynamics and control of evolutionary networked games with multi-group[C]//Proceedings of the 35th Chinese Control Conference. Chengdu, China, 2016: 585–590. [18] GUO Peilian, WANG Yuzhen, LI Haitao. Algebraic for￾mulation and strategy optimization for a class of evolu￾tionary networked games via semi-tensor product method[J]. Automatic, 2013, 49(11): 3384–3389. [19] ZHAO Guodong, WANG Yuzhen. Formulation and op￾timization control of a class of networked evolutionary games with switched topologies[J]. Nonlinear analysis: hybrid systems, 2016, 22: 98–107. [20] ZHU Bing, XIA Xiaohua, WU Zhou. Evolutionary game theoretic demand-side management and control for a class [21] 第 5 期 武利琴，等：基于半张量积的企业创新网络演化博弈 ·781·