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...</citationref></citationref>

First, we suggest and discuss second-order versions of properties for solutions for TU games used to characterize the Banzhaf value, in particular, of standardness for two-player games, of the dummy player property, and of 2-efficiency. Then, we provide a number of characterizations of the...