Gain-Loss, Sign Differential Marginality and the Shapley Value

We revisit the characterization of the Shapley value by Casajus (Math Soc Sci 68 (2014) 1-4) via the gain-loss property (Einy and Haimanko, 2011), differential marginality and the dummy player property. We first show that differential marginality in this characterization can be weakened into sign differential marginality (Casajus, 2017). Second, we show that the gain-loss property, together with sign symmetry (Casajus, 2018), marginality and the inessential game property, characterizes the Shapley value