基于限制合作博弈的产业集群企业利益分配研究

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。

Study on Profit Allocation of Industrial Cluster Based on Restricted Cooperative Game

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.