具有合作限制的合作对策理论及应用研究

In classical cooperative game theory, it is assumed that every coalition of players can be formed and gains an exact benefit. However, in various economic and social situations, it is possible that some of players are unable to work together, and every subset of players gains an exact benefit that is inappropriate. This project will be focus on the subject of cooperative games with restricted cooperation, mainly from three aspects: (1) some fuzzy phenomenon in cooperation, (2) the worth of a coalition may depend on the order in which the coalition is being formed, (3) endogenous information contained in the set of feasible coalitions. The first two aspects are considered when the formation of a coalition is related to the order of players, and the third one is considered when coalition formed without restriction of order of players. Therefore, the project is mainly studied in three directions. Firstly, based on fuzzy mathematics, graph theory and fraction graph theory, the fuzzy-valued cooperative games with permission structure and the cooperative games with fuzzy permission structure are studied. Meanwhile, those games with risk preferences/thresholds are also investigated. Secondly, based on the properties of cycle-free directed graph, the games in generalized characteristic function with restricted cooperation are considered, and then this class of games is studied from the perspective of cooperation preferences among players. Thirdly, considering the theories of non-additive measures and graph theory, we quantitative analysis the information in the set of feasible coalitions, and this information is used to study cooperative games with arbitrary feasible coalitions. The above researches are focus on distribution of the payoffs among players, as well as the interaction among players and the stability of coalition..The research of this project aims to enrich and to perfect the theory of cooperative games with restricted cooperation, and to provide decision making strategies for practical problems.

经典合作对策假设所有联盟都能形成并获得精确的收益，但是现实中合作通常有限制且收益是复杂的。本项目将对具有合作限制的合作对策展开研究，主要从三个角度：(1)合作中存在模糊性、(2)联盟收益与结盟顺序有关、(3)联盟包含隐藏信息，其中前两个是针对结盟与局中人顺序有关的情形，后一个是针对结盟与局中人顺序无关的情形。为此，主要进行三个方面研究：第一，对具有许可结构的合作对策利用模糊数学、图论和分数图论从模糊支付与模糊联盟展开研究，并将风险偏好、阈值引入到模型。第二，对具有广义特征函数且合作受限制的合作对策借鉴无环有向图的性质展开研究，并基于局中人的合作偏好进行考虑。第三，探究联盟形成是无规律的合作对策，并结合非可加测度与图论从联盟信息视角展开研究。以上研究均以收益分配问题为中心，并兼顾局中人相互关系和联盟稳定性的研究。.通过本项目的研究，丰富完善具有合作限制的合作对策理论，为解决实际问题提供依据。

本项目对具有合作限制的合作对策展开研究，主要从以下五个方面：1、在基于模糊支付与模糊联盟的合作对策研究中，提出模糊联盟合作对策的一致形式，并采用公理化方法研究了模糊核心、模糊稳定集、模糊Shapley值、强模糊核心、模糊Owen值并讨论其性质和应用；2、在具有限制联盟结构及优先联盟的合作对策研究中，重点讨论了有联盟限制且局中人具有权重的合作对策的解， 研究M-限制合作对策的最小二乘解的公理系统，提出了在具有限制联盟的可加属性合作对策上的分支资源解(BR值)并公理化，讨论了权限结构对优先联盟内合作的限制的两阶段Shapley值的性质，以及对具有T-联盟结构的Shapley值的性质；3、在基于联盟形成的合作对策解的研究中，重点研究了一类具有可加属性的合作对策的解，提出对称最小二乘解并讨论其性质，引入一类比例剩余划分值并讨论其性质，同时研究了比例划分值的公理化特征；4、在物流供应链决策应用研究中，主要研究了从消费者、制造商和零售商等不同角度在不确定环境下的绿色供应链的产品定价、优化策略问题，分析了在区块链驱动下快递企业是否共同配送的策略选择问题，还研究了无供应商的最小生成树的成本分配问题；5、在其他相关研究中，提出一种描述多属性合作对策中的联盟集合的联盟多项式，探讨Pythagorean模糊Hamacher集结算子问题等。本项目研究成果完善了具有合作限制的合作对策的收益分配理论和联盟形成理论，特别是具有模糊支付和模糊联盟的合作对策以及具有联盟限制的合作对策的理论体系建设，为解决相应的实际问题提供理论指导和决策依据。在本项目的支持下，项目组成员在国际、国内核心期刊上发表学术论文25篇，其中被SCI/SSCI收录11篇，被EI收录5篇，中文核心12篇，CSSCI4篇。培养出(已毕业)与对策论研究方向有关的博士2名，硕士2名。总之，该项目进展顺利，达到了预期的效果。

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