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, 1994) and Malawski (Int J Game Theory 31:47–67, 2002). Within these characterizations, any of the collusion properties can be replaced by additivity and the quarrel property due to the latter author.
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We are indebted to Frank Huettner for helpful discussions on the matter.
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Casajus, A. Collusion, quarrel, and the Banzhaf value. Int J Game Theory 43, 1–11 (2014). https://doi.org/10.1007/s00182-012-0364-4