在无循环可访问的工会上,稳定的网络结构稳定
Encarnación Algaba1, René van den Brink2, Chris Dietz2
1Matemática Aplicada II and Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Escuela Superior de Ingenieros, Camino de los Descubrimientos, s/n, 41092 Sevilla, Spain.
概括
我们确定了在无循环网络中连接的联盟的独特集合理论属性. 这导致了一个新的"平衡公平"公理,它与组件效率一起,独特地定义了合作游戏的Shapley值.
科学领域:
- 合作游戏理论 合作游戏理论
- 网络结构 网络结构 网络结构
- 图形理论是指图形的理论.
背景情况:
- 了解网络中的联盟形成对于合作游戏理论至关重要.
- 现有的框架往往缺乏针对无循环网络结构的具体特征.
- 沙普利值是合作游戏中一个突出的解决方案概念.
研究的目的:
- 在可访问的联盟稳定网络结构中,在无循环无定向图中识别特征连接联盟的集合理论属性.
- 在这些特定的网络结构上为合作游戏定义一个新的公平公理.
- 用这个新的公理和组件效率来描述沙普利值.
主要方法:
- 调查联盟的集合理论属性.
- 分析可行的联盟作为支持联盟的独特表示.
- 定义和应用一个新的公平公理 ("平衡的公平").
主要成果:
- 在无循环网络中的连接联盟表现出特定的集合理论属性.
- 发现了非统一可行的联盟作为非统一支持的联盟的独特代表性.
- 一个新的"平衡的公平性"公理,结合组件效率,独特地描述了沙普利价值.
结论:
- 该研究提供了无循环网络中的联盟的精确特征.
- "平衡公平"公理为合作游戏理论中的解决方案概念提供了新的视角.
- 沙普利价值是由这些网络上的组件效率和平衡公平性独一无二地决定的.
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