In this paper we generalize the graph Banzhaf value, proposed by Alonso-Meijide and Fiestras-Janeiro (Naval Res Logist 53(3):198–203, 2006) in the deterministic communication situations, to the generalized probabilistic communication situations. This new value is called the probabilistic Banzhaf value. We provide two axiomatic characterizations of the value by the probabilistic versions of component total power, fairness and balanced contributions. Furthermore, we give an alternative characterization of the value by using the probabilistic player potential function.

中文翻译：

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广义概率交流情况的Banzhaf值

在本文中，我们将由Alonso-Meijide和Fiestras-Janeiro（Naval Res Logist 53（3）：198-203，2006）提出的在确定性通信情况下的Banzhaf值图推广到广义概率通信情况。这个新值称为概率Banzhaf值。我们通过组件总功率，公平性和平衡贡献的概率版本提供了两个公理化的价值表征。此外，我们通过使用概率玩家潜力函数来给出值的替代表征。