具有流结构的合作博弈及其应用
Cooperative Games with Network Flow Structure and Its Application
摘要: 本文讨论了一类具有联盟受限的合作博弈问题，在经典可转移效用合作博弈的基础上引入有向网络结构，提出了具有流限制的合作博弈模型，简称流博弈。随后，基于Shapley值和有向图限制结构定义了流博弈的一个解，并对其性质进行了分析。通过对有效性以及公平性等性质的扩展，给出了流博弈分配规则的一个公理刻画。最后，将流博弈及其分配规则应用在跨国公益物资运输问题中，构建了成本运输分摊博弈模型，并通过算例分析了流博弈及其分配规则的合理性。
Abstract: This paper introduces flow structure constraints and puts forward a cooperative game with flow structure (flow games for short). And then, the Shapley value is used to define a solution concept, called flow value, for the class of flow games, and the axiomatization of the new value is proposed by efficiency and flow fairness. Finally, flow games and the flow value are applied to the transnational public welfare supplies problem, and the rationality of the game model and allocation rule is ana-lyzed as an aspect of applications.
文章引用：葛静沂, 张广. 具有流结构的合作博弈及其应用[J]. 理论数学, 2022, 12(12): 2141-2152. https://doi.org/10.12677/PM.2022.1212230

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