交流网络和层次结构双重限制下合作博弈的公平分配机制研究

The establishment of a fair allocation mechanism is a pressing issue during social transformation. To this issue, cooperative game theory can offer solutions. However, with the developments of science, technology, and social economics, fair allocation is affected by more and more factors, and the classical cooperative game theory is increasingly inapplicable. To mitigate this, the present project is devoted to a new class of cooperative games, cooperative games restricted by both a communication network and a level structure, in which the communication network and the level structure respectively describe the communication channels among players and the structures of organizations. Since both communication and organization structure affect fair allocation, the new class of games is more suitable to the real world. We focus on fair allocation mechanisms of this class of games. Particularly, we propose two types of mechanisms, which are respectively based on the network restricted game and the level restricted game. To justify them, after giving explicit expression of every mechanism, we analyze their axiomatic features and characterize them with the axiomatic method. As applications, the proposed mechanisms are applied to the field of network sciences, and therein new measures of network centralities are obtained. Research results can enrich, deepen, and unite results in related classes of cooperative games, provide new solutions to fair allocation, and support network analysis.

社会转型过程中，公平分配机制的建立是一个重要问题。合作博弈理论可为其提供解决方案。然而，随着科学技术和社会经济的发展，影响公平分配的因素日益增多，传统的合作博弈理论已难以适应当前的社会需要。项目研究交流网络和层次结构双重限制下的合作博弈。它是一种新兴类别的合作博弈，其中交流网络描述局中人间的交流通道，层次结构描述组织的结构。由于交流和组织结构都会影响公平分配，这类博弈具有很强的现实适应性。项目致力于这类博弈的公平分配机制研究。通过分别对该类博弈取网络限制博弈和层次限制博弈，构造它的两类公平分配机制。为说明各公平分配机制的公平性，在给出其显示解析表达式定义基础上，进一步揭示其公理化特征，并依据特征对其进行公理化刻画。通过将公平分配机制应用到网络科学，构造新的网络节点重要性测度。研究结果可丰富、深化和统一多种相关类别合作博弈的研究成果，为公平分配问题提供新的解决方案，并为网络分析提供方法支持。

社会转型过程中，公平分配机制的建立是一个重要问题。合作博弈理论可为这一问题提供解决方案。然而，随着科学技术和社会经济的发展，影响公平分配的因素日益增多，传统的合作博弈理论已难以适应当前的社会需要。. 项目研究具有交流网络和层次结构双重限制的合作博弈。这是一种新兴类别的合作博弈，其中交流网络描述局中人之间的交流通道，层次结构则描述组织的结构。由于交流和组织结构都会影响分配过程，这类博弈具有很强的现实适应性。项目致力于这类博弈的公平分配机制研究。通过分别对该类博弈取图限制博弈和层次限制博弈，构造它的两类分配机制。为说明各分配机制的公平性，在给出其显示解析表达式定义的基础上，进一步揭示其公理化特征，并依据特征对其进行公理化刻画。通过将分配机制应用到网络科学，构造新的网络节点重要性测度。. 围绕这些研究内容，项目已公开资助出版学术论文4篇，均被SCI/SSCI收录，均发表于FMS管理科学部推荐期刊，且其中3篇发表于ABS三星级期刊。另有审稿中论文2篇，工作论文1篇，拟出版学术专著1部。较圆满的完成了预期任务。. 研究结果可丰富、深化和统一多种相关类别合作博弈的研究成果，为公平分配问题提供新的解决方案，并为网络分析提供方法支持。