基于限制合作博弈的产业集群企业利益分配研究
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摘要
产业集群内部企业组成协同创新联盟是促进联盟合作的有效途径,然而影响联盟企业合作最为关键的因素是如何合理公平的对联盟的利益进行分配。考虑联盟中企业合作能力为灰色信息且企业之间的依赖关系具有不完整性,本文首先,基于灰色系统理论定义了灰色授权算子;其次,运用Choquet积分对企业之间的依赖关系进行集成;再将这种依赖关系信息和Shapley模型结合起来建立了具有灰色授权机制的限制合作博弈模型,并证明了该模型满足有效性、对称性、可加性和哑元性公理。最后通过算例说明了该模型的可行性和实用性。
The most critical factor affecting alliance enterprise cooperation is how to distribute the benefits obtained from forming alliances reasonably and fairly.The rationality of interest distribution directly affects the sustainability and stability of alliance innovation.How to effectively solve the problem of distribution of income within a cooperative alliance has become an important topic at domestic and abroad.The traditional Shapley value method assumes that each member of the cooperative alliance has the same marginal contribution as the premise.However,in the actual situation,due to the limitations of the self-generated technology and the uncertainty of the industrial cluster environment,the enterprise can only play a part of their capacities.At the same time,it is difficult for enterprises to fully identify the exact value of information.In order to solve the above problems,the restricted cooperation games is studied in this paper,in which the cooperation ability is the gray information and the dependency relationships among the enterprises that restrict their capacity to cooperate within some coalitions.First of all,the gray authorization operator based on the grey system theory is defined.Secondly,the Choquet integrals are used to integrate the dependencies between enterprises.And then,this dependency information is combined with the Shapley model to establish a restricted cooperative game model with gray authorization mechanism.And it is proved that the model satisfies the efficiency,symmetry,additivity and dummy player axioms.Finally,an example is given to illustrate the feasibility and practicality of the model.
The most critical factor affecting alliance enterprise cooperation is how to distribute the benefits obtained from forming alliances reasonably and fairly.The rationality of interest distribution directly affects the sustainability and stability of alliance innovation.How to effectively solve the problem of distribution of income within a cooperative alliance has become an important topic at domestic and abroad.The traditional Shapley value method assumes that each member of the cooperative alliance has the same marginal contribution as the premise.However,in the actual situation,due to the limitations of the self-generated technology and the uncertainty of the industrial cluster environment,the enterprise can only play a part of their capacities.At the same time,it is difficult for enterprises to fully identify the exact value of information.In order to solve the above problems,the restricted cooperation games is studied in this paper,in which the cooperation ability is the gray information and the dependency relationships among the enterprises that restrict their capacity to cooperate within some coalitions.First of all,the gray authorization operator based on the grey system theory is defined.Secondly,the Choquet integrals are used to integrate the dependencies between enterprises.And then,this dependency information is combined with the Shapley model to establish a restricted cooperative game model with gray authorization mechanism.And it is proved that the model satisfies the efficiency,symmetry,additivity and dummy player axioms.Finally,an example is given to illustrate the feasibility and practicality of the model.
引文
[1]Shapley L S.A value for n-person games[M]//Kuhn H,Tucker A W.Contributions to the theory of gamesⅡ.Princeton:Princeton University Press,1953.
[2]Aumann R J,Maschler M.The bargaining set for cooperative games[J].Advances in Game Theory,1964,52:443-476.
[3]Myerson R B.Graphs and cooperation in games[J].Mathematics of Operations Research,1977,2:225-229.
[4]Gilles R P,Owen G,van den Brink R.Games with permission structures:The conjunctive approach[J].International Journal of Game Theory,1992,20:277-293.
[5]Derks J J M,Gilles R P.Hierarchical organization structures and constraints on coalition formation[J].International Journal of Game Theory,1995,24:147-163.
[6]Derks J J M,Reijnierse H.On the core of a collection of coalitions[J].International Journal of Game Theory,1998,27:451-459.
[7]Béal S,Rémila E,Solal P.Rooted-tree solutions for tree games[J].European Journal of Operational Research,2010,203(2):404-408.
[8]Herings P,van der Laan G,Talman D.The average tree solution for cycle free games[J].Games and Economic Behavior,2008,62:77-92.
[9]孙红霞,张强.具有联盟结构的限制合作博弈的限制Owen值[J].系统工程理论与实践,2013,33(4):981-987.
[10]Faigle U,Kern W.The Shapley value for cooperative games under precedence constraints[J].International Journal of Game Theory,1992,21:249-266.
[11]张瑜,菅利荣,刘思峰,等.基于优化Shapley值的产学研网络型合作利益协调机制研究[J].中国管理科学,2016,24(9):36-44.
[12]Choquet G.Theory of capacities[C].Annales de l’institut Fourier,1954,5:131-292.
[13]赵树平,梁昌勇,罗大伟.基于VIKOR和诱导广义直觉梯形模糊Choquet积分算子的多属性群决策方法[J].中国管理科学,2016,24(6):132-142.
[14]Gallardo J M,Jiménez N,Jiménez-Losada A,et al.Games with fuzzy authorization structure:A Shapley value[J].Fuzzy Sets and Systems,2015,272:115-125.
[15]孙红霞,张强.具有模糊联盟博弈的Shapley值的刻画[J].系统工程理论与实践,2010,30(8):1457-1464.
[16]孙红霞.基于Chouqet积分形式的模糊联盟核心[J].运筹与管理,2015,24(1):93-99.
[17]孟凡永,张强.具有Choquet积分形式的模糊合作对策[J].系统工程与电子技术,2010,33(4):981-987.
[18]单而芳,张广.准许树博弈的权重准许分支公平和准许树限制核[J].系统工程理论与实践,2017,37(7):1752-1760.
[19]杨靛青,李登峰,俞裕兰.模糊联盟图合作对策(值[J].控制与决策,2017,32(9):1653-1758.
[20]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002:70-71.
[21]闫书丽,刘思峰,朱建军,等.基于相对核和精确度的灰数排序方法[J].控制与决策,2014,29(2):315-319.
[22]王大澳,菅利荣,刘思峰,等.基于Choquet积分的多属性灰靶群决策方法[J].控制与决策,2017,32(7):1286-1292.
[23]汪贤裕,肖玉明.博弈论及其应用[M].北京:科学出版社,2008.
[2]Aumann R J,Maschler M.The bargaining set for cooperative games[J].Advances in Game Theory,1964,52:443-476.
[3]Myerson R B.Graphs and cooperation in games[J].Mathematics of Operations Research,1977,2:225-229.
[4]Gilles R P,Owen G,van den Brink R.Games with permission structures:The conjunctive approach[J].International Journal of Game Theory,1992,20:277-293.
[5]Derks J J M,Gilles R P.Hierarchical organization structures and constraints on coalition formation[J].International Journal of Game Theory,1995,24:147-163.
[6]Derks J J M,Reijnierse H.On the core of a collection of coalitions[J].International Journal of Game Theory,1998,27:451-459.
[7]Béal S,Rémila E,Solal P.Rooted-tree solutions for tree games[J].European Journal of Operational Research,2010,203(2):404-408.
[8]Herings P,van der Laan G,Talman D.The average tree solution for cycle free games[J].Games and Economic Behavior,2008,62:77-92.
[9]孙红霞,张强.具有联盟结构的限制合作博弈的限制Owen值[J].系统工程理论与实践,2013,33(4):981-987.
[10]Faigle U,Kern W.The Shapley value for cooperative games under precedence constraints[J].International Journal of Game Theory,1992,21:249-266.
[11]张瑜,菅利荣,刘思峰,等.基于优化Shapley值的产学研网络型合作利益协调机制研究[J].中国管理科学,2016,24(9):36-44.
[12]Choquet G.Theory of capacities[C].Annales de l’institut Fourier,1954,5:131-292.
[13]赵树平,梁昌勇,罗大伟.基于VIKOR和诱导广义直觉梯形模糊Choquet积分算子的多属性群决策方法[J].中国管理科学,2016,24(6):132-142.
[14]Gallardo J M,Jiménez N,Jiménez-Losada A,et al.Games with fuzzy authorization structure:A Shapley value[J].Fuzzy Sets and Systems,2015,272:115-125.
[15]孙红霞,张强.具有模糊联盟博弈的Shapley值的刻画[J].系统工程理论与实践,2010,30(8):1457-1464.
[16]孙红霞.基于Chouqet积分形式的模糊联盟核心[J].运筹与管理,2015,24(1):93-99.
[17]孟凡永,张强.具有Choquet积分形式的模糊合作对策[J].系统工程与电子技术,2010,33(4):981-987.
[18]单而芳,张广.准许树博弈的权重准许分支公平和准许树限制核[J].系统工程理论与实践,2017,37(7):1752-1760.
[19]杨靛青,李登峰,俞裕兰.模糊联盟图合作对策(值[J].控制与决策,2017,32(9):1653-1758.
[20]邓聚龙.灰理论基础[M].武汉:华中科技大学出版社,2002:70-71.
[21]闫书丽,刘思峰,朱建军,等.基于相对核和精确度的灰数排序方法[J].控制与决策,2014,29(2):315-319.
[22]王大澳,菅利荣,刘思峰,等.基于Choquet积分的多属性灰靶群决策方法[J].控制与决策,2017,32(7):1286-1292.
[23]汪贤裕,肖玉明.博弈论及其应用[M].北京:科学出版社,2008.