Necessary versus equal players in axiomatic studies

This note introduces three variants of existing axioms in which equal players are replaced by necessary players. We highlight that necessary players can replace equal players in many wellknown axiomatic characterizations, but not in all. In addition, we provide new characterizations of the Shapley value, the class of positively weighted Shapley values, the Solidarity value and the Equal Division value. This sheds a new light on the real role of equal treatment of equals in the axiomatic literature.