On a family of values for TU-games generalizing the Shapley value

In this paper we study a family of efficient, symmetric and linear values for TU-games, described by some formula generalizing the Shapley value. These values appear to have surprising properties described in terms of the axioms: Fair treatment, monotonicity and two types of acceptability. The results obtained are discussed in the context of the Shapley value, the solidarity value, the least square prenucleolus and the consensus value.

► A family of values for TU-games generalizing the Shapley value is studied.
► Axioms: fair treatment, monotonicity and two types of acceptability properties are considered.
► Values are studied in the context of different configurations of these axioms.
► Surprising formulae for values are found.
► Shapley value, solidarity value, the least square prenucleolus and consensus value are discussed.