The Banzhaf value for generalized probabilistic communication situations

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.