模糊网络博弈的合作联盟优化对策研究
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摘要
模糊网络博弈主要关注如何将联盟收益分配给合作联盟的每个参与者,其广义模糊博弈解同时引入参与度和调整系数,不仅实现了参与者以部分资源参与合作联盟的愿望,而且满足了保留部分收益值用于联盟再发展的需求.本文作为模糊博弈模型的后续深入研究,对模糊网络博弈的解进行拓展,提出广义模糊核心解、广义模糊谈判集解的概念,并证明当满足超可加性的前提下,模糊网络博弈的广义模糊核心解与其广义模糊谈判集解具有等价关系,并刻画了模糊网络博弈广义核心解的非空性,算例分析结果表明合作联盟广义分配方案的存在性,为合作联盟优化对策提供服务.
The fuzzy network cooperative game mainly studies how to distribute the cooperative coalition profit to each participant of the network coalition, the generalized fuzzy game theory with participation and adjustment coefficients is introduced, which not only achieves the desire of participants to participate in cooperative alliances with some resources,but also meets the needs of preserving part of the value of income for the redevelopment of alliances. Further study of this article as the fuzzy game model, the solutions of fuzzy network game are extended, the definition of generalized fuzzy imputation, generalized fuzzy core and generalized fuzzy bargaining set are proposed, and it is proved that the generalized fuzzy core of the fuzzy network cooperative game is equivalent to the generalized fuzzy bargaining set when the super additive is satisfied. The nonempty of the solution of generalized fuzzy core in network cooperative game is described.Example analysis results show the existence and rationality of the generalized distribution scheme, it provides service for cooperative alliance optimization strategy.
The fuzzy network cooperative game mainly studies how to distribute the cooperative coalition profit to each participant of the network coalition, the generalized fuzzy game theory with participation and adjustment coefficients is introduced, which not only achieves the desire of participants to participate in cooperative alliances with some resources,but also meets the needs of preserving part of the value of income for the redevelopment of alliances. Further study of this article as the fuzzy game model, the solutions of fuzzy network game are extended, the definition of generalized fuzzy imputation, generalized fuzzy core and generalized fuzzy bargaining set are proposed, and it is proved that the generalized fuzzy core of the fuzzy network cooperative game is equivalent to the generalized fuzzy bargaining set when the super additive is satisfied. The nonempty of the solution of generalized fuzzy core in network cooperative game is described.Example analysis results show the existence and rationality of the generalized distribution scheme, it provides service for cooperative alliance optimization strategy.
引文
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[10] ZHENG Yuelong. Study on formation mechanism of generic technology cooperative R&D based on evolutionary game theory.Chongqing:Chongqing University, 2015.(郑月龙.基于演化博弈论的企业共性技术合作研发形成机制研究.重庆:重庆大学, 2015.)
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[12] YI Yuyin, SHENG Zhaohan, XIAO Tiaojun. Evolutionary game analysis of cournot competition with different behavior rule. Chinese Journal of Management Science, 2004, 12(3):125–129.(易余胤,盛昭瀚,肖条军.不同行为规则下的Cournot竞争的演化博弈分析.中国管理科学, 2004, 12(3):125–129.)
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[16] LI Cui, XUE Huifeng. Research on sustainable development strategy of enterprise knowledge alliance—from the perspective of benefit distribution. Technoeconomics&Management Research, 2016, 12(1):3–8.(李翠,薛惠锋.企业知识联盟的可持续发展对策研究――以利益分配为视角.技术经济与管理研究, 2016, 12(1):3–8.)
[17] LI Xianyin, CHEN Wanming. An evolutionary game model for knowledge sharing in the organization. Statistics and Decision, 2008,1(12):170–171.(李宪印,陈万明.组织内知识共享的进化博弈模型.统计与决策,2008, 1(12):170–171.)
[18] SUN Hongxia, ZHANG Qiang. Scheme of profit allocation based on fuzzy cooperative game in coalition structure. Operations Research and Management Science, 2010, 19(5):84–89.(孙红霞,张强.基于联盟结构的模糊合作博弈的收益分配方案.运筹与管理, 2010, 19(5):84–89.)
[19] PETERS H, VERMEULEN D. WPO, COV and IIA bargaining solutions for non-convex bargaining problems. International Journal of Game Theory, 2012, 41(4):851–884.
[20] QIN C Z, SHI S, TAN G. Nash bargaining for log-convex problems.Economic Theory, 2015, 58(3):413–440.
[21] LIU Xiaodong, LIU Jiuqiang, HU Jian. On cooperative games with restricted payoffs. Acta Mathematicae Applicatae Sinica, 2012,35(5):845–854.(刘小冬,刘九强,胡健.具有受限支付的合作博弈研究.应用数学学报, 2012, 35(5):845–854.)
[22] LIU J, ZHANG H. Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy. International Journal of Games Theory, 2015, 45(4):1–15.
[23] GRANOT D, GRANOT F. On some network flow games. Mathematics of Operations Research, 1992, 17(4):792–841.
[24] OKADA A. Cooperation and institution in games. The Japanese Economic Review, 2015, 66(1):1–32.
[25] WANG Fengye, HUANG Zhiyong, SHANG Youlin, et al. A kind of fuzzy cooperative game and its core. Journal of Henan University of Science and Technology:Natural Science. 2014, 35(1):75–78.(王锋叶,黄志勇,尚有林,等.一类模糊合作博弈及其核心.河南科技大学学报自然科学版, 2014, 35(1):75–78.)
[26] SAWA R. Coalitional stochastic stability in games, networks and markets. Games&Economic Behavior, 2014, 88(C):90–111.
[2] SHIN D H, SHIN Y J. Why do people play social network games?Computers in Human Behavior, 2011, 27(2):852–861.
[3] LI Cui, XUE Yu, WANG Wensheng. Model of profit reallocation based on generalized solution in average monotonic game. Control and Decision, 2015, 30(4):645–654.(李翠,薛昱,王文胜.基于平均单调博弈广义解的收益再分配模型.控制与决策, 2015, 30(4):645–654.)
[4] SUN Xinbo, LIU bo. A study on the relation of knowlege alliance incentive synergy order parameter base on the structural equation.Chinese Journal of Management, 2012, 9(12):1826–1831.(孙新波,刘博.基于结构方程模型的知识联盟激励协同序参量关系研究.管理学报, 2012, 9(12):1826–1831.)
[5] BORKOTOKEY S, GOGOI L, SARANGI S. A survey of player based and link based allocation rules for network games. Studies in Microeconomics, 2014, 2(2):5–26.
[6] CAULIER J F, GRABISCH M, RUSINOWSKA A. An allocation rule for dynamic random network formation processes. Economic Theory, 2015, 60(2):283–313.
[7] LI Cui, XUE Yu. Scheme of profit allocation based on fuzzy cooperative game in bargaining set. Control and Decision, 2014, 29(11):2101–2107.(李翠,薛昱.基于谈判集的模糊合作博弈的收益分配方案.控制与决策, 2014, 29(11):2101–2107.)
[8] LI Yunyao, SHENG Yanchao, JIANG Xiangyang. Alliance motivation, technology capability and the optimal strategy of enterprises joining the alliance. Management World, 2010, 3(3):178–179.(李允尧,生延超,姜向阳.联盟动机、技术能力与企业入盟的最优策略.管理世界. 2010, 3(3):178–179.)
[9] LIU Erliang, JI Yanbin. Research on game theory of knowledge sharing in knowledge alliance with incomplete information. Journal of Southwest Jiaotong University, 2011, 12(6):83–88.(刘二亮,纪艳彬.不完全信息下知识联盟内知识共享博弈研究.西南交通大学学报, 201l, 12(6):83–88.)
[10] ZHENG Yuelong. Study on formation mechanism of generic technology cooperative R&D based on evolutionary game theory.Chongqing:Chongqing University, 2015.(郑月龙.基于演化博弈论的企业共性技术合作研发形成机制研究.重庆:重庆大学, 2015.)
[11] IMAI H, SALONEN H. A characterization of a limit solution for finite horizon bargaining problems. International Journal of Game Theory, 2012, 41(3):603–622.
[12] YI Yuyin, SHENG Zhaohan, XIAO Tiaojun. Evolutionary game analysis of cournot competition with different behavior rule. Chinese Journal of Management Science, 2004, 12(3):125–129.(易余胤,盛昭瀚,肖条军.不同行为规则下的Cournot竞争的演化博弈分析.中国管理科学, 2004, 12(3):125–129.)
[13] ZHANG Wei, GENG Shengling, TONG Yinghua, et al. Income distribution based on fuzzy soft cooperative game. Journal of Jiangsu Normal University:Natural Science Edition, 2016, 34(2):37–41.(张炜,耿生玲,童英华,等.基于模糊软合作博弈的收益分配.江苏师范大学学报(自然科学版), 2016, 34(2):37–41.)
[14] AVRACHENKOV K, SINGH V V. Stochastic coalitional betterresponse dynamics and stable equilibrium. Automation&Remote Control, 2016, 77(12):2227–2238.
[15] LI Quanlin, DUAN Can, E Chengguo, et al. Rearch on cooperative game and revenue allocation in cloud federation platform. Operations Research and Management Science, 2014, 23(4):274–279.(李泉林,段灿,鄂成国,等.云资源提供商的合作博弈模型与收益分配研究.运筹与管理, 2014, 23(4):274–279.)
[16] LI Cui, XUE Huifeng. Research on sustainable development strategy of enterprise knowledge alliance—from the perspective of benefit distribution. Technoeconomics&Management Research, 2016, 12(1):3–8.(李翠,薛惠锋.企业知识联盟的可持续发展对策研究――以利益分配为视角.技术经济与管理研究, 2016, 12(1):3–8.)
[17] LI Xianyin, CHEN Wanming. An evolutionary game model for knowledge sharing in the organization. Statistics and Decision, 2008,1(12):170–171.(李宪印,陈万明.组织内知识共享的进化博弈模型.统计与决策,2008, 1(12):170–171.)
[18] SUN Hongxia, ZHANG Qiang. Scheme of profit allocation based on fuzzy cooperative game in coalition structure. Operations Research and Management Science, 2010, 19(5):84–89.(孙红霞,张强.基于联盟结构的模糊合作博弈的收益分配方案.运筹与管理, 2010, 19(5):84–89.)
[19] PETERS H, VERMEULEN D. WPO, COV and IIA bargaining solutions for non-convex bargaining problems. International Journal of Game Theory, 2012, 41(4):851–884.
[20] QIN C Z, SHI S, TAN G. Nash bargaining for log-convex problems.Economic Theory, 2015, 58(3):413–440.
[21] LIU Xiaodong, LIU Jiuqiang, HU Jian. On cooperative games with restricted payoffs. Acta Mathematicae Applicatae Sinica, 2012,35(5):845–854.(刘小冬,刘九强,胡健.具有受限支付的合作博弈研究.应用数学学报, 2012, 35(5):845–854.)
[22] LIU J, ZHANG H. Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy. International Journal of Games Theory, 2015, 45(4):1–15.
[23] GRANOT D, GRANOT F. On some network flow games. Mathematics of Operations Research, 1992, 17(4):792–841.
[24] OKADA A. Cooperation and institution in games. The Japanese Economic Review, 2015, 66(1):1–32.
[25] WANG Fengye, HUANG Zhiyong, SHANG Youlin, et al. A kind of fuzzy cooperative game and its core. Journal of Henan University of Science and Technology:Natural Science. 2014, 35(1):75–78.(王锋叶,黄志勇,尚有林,等.一类模糊合作博弈及其核心.河南科技大学学报自然科学版, 2014, 35(1):75–78.)
[26] SAWA R. Coalitional stochastic stability in games, networks and markets. Games&Economic Behavior, 2014, 88(C):90–111.