Collusion, quarrel, and the Banzhaf value

We provide new, concise characterizations of the Banzhaf value on a fixed player set employing just the standard dummy player property and one of the collusion properties suggested by Haller (Int J Game Theory 23:261–281, <CitationRef CitationID="CR8">1994</CitationRef>) and Malawski (Int J Game Theory 31:47–67, <CitationRef CitationID="CR11">2002</CitationRef>). Within these characterizations, any of the collusion properties can be replaced by additivity and the quarrel property due to the latter author. Copyright Springer-Verlag Berlin Heidelberg 2014