Gain–loss and new axiomatizations of the Shapley value

The aim of this paper is to provide new axiomatizations of the Shapley value that generalize previous characterizations. The first characterization employs the gain–loss property, sign differential marginality and the dummy player property. In the second axiomatization, we use the axioms of the gain–loss property, sign symmetry, marginality and the inessential game property. Finally, we introduce the sign marginality property and characterize the Shapley value by combining the property with the other properties.