We suggest new characterizations of the Banzhaf value without the symmetry axiom, which reveal that the characterizations by Lehrer (1988, International Journal of Game Theory 17, 89-99) and Nowak (1997, International Journal of Game Theory 26, 127-141) as well as most of the characterizations...

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>

We resolve redundancies in the characterizations of the Banzhaf value suggested by Haller (1994, Int J Game Theory 23, 261-281) and Malawski (2002, Int J Game Theory 31:47-67). In particular, we show that the collusion properties employed by them are equivalent. Combined with the dummy player...

We suggest new characterizations of the Banzhaf value without the symmetry axiom, which reveal that the characterizations by Lehrer (1988, International Journal of Game Theory 17, 89-99) and Nowak (1997, International Journal of Game Theory 26, 127-141) as well as most of the characterizations...

We show that the Owen value for TU games with a cooperation structure extends the Shapley value in a consistent way. In particular, the Shapley value is the expected Owen value for all symmetric distributions on the partitions of the player set. Similar extensions of the Banzhaf value do not...

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...