联盟信息缺失下的合作博弈比例分离解及其应用
The Proportional Split-Off Solution and Application for Cooperative Games in the Missing Information of Coalitions
摘要: 本文研究了合作博弈理论，在部分联盟信息缺失的基础上将联盟形成过程和比例分配结合起来，提出了部分联盟信息缺失下的比例分离解的概念。首先，在部分联盟信息缺失的情况下利用给定的权重，依据回报率高的联盟先加入大联盟，得出大联盟合适的划分，之后按照加入顺序对划分联盟的边际贡献基于权重进行比例分配。其次，在公理刻画部分基于最高回报一致性进行了研究，得出三个刻画定理。最后，将新的解概念应用到区域建设问题中，以一带一路某地区为例，分析了该地区修建高铁时各国合理的出资比例。
Abstract: This paper studies the theory of cooperative games, combines the coalition formation process and proportional allocation on the basis of partial coalition information missing, and proposes the concept of proportional split-off solution under partial coalition information missing. Firstly, in the missing information of some coalitions, using the given weights, the coalition with high return rate joins the big coalition first, thus obtaining the appropriate division of the big coalition, and then according to the order of joining the marginal contribution of the divided coalition based on the proportional allocation of the weights. Secondly, in the axiomatic characterization section, three characterization theorems are derived based on the highest payoff consistency. Finally, the new solution concept is applied to the regional construction problem, and the reasonable contribution ratio of each country in the construction of high-speed rail in a region of The Belt and Road is analyzed as an example.
文章引用：王佳颖, 张广. 联盟信息缺失下的合作博弈比例分离解及其应用[J]. 运筹与模糊学, 2024, 14(3): 301-312. https://doi.org/10.12677/orf.2024.143268

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