Axiomatic characterizations of the weighted solidarity values

• We define and characterize the family of all weighted solidarity values.
• We present two axiomatizations, one with additivity, and the other, without it.
• We study the behavior of these values in the class of monotonic games.

We define and characterize the class of all weighted solidarity values. Our first characterization employs the classical axioms determining the solidarity value (except symmetry), that is, efficiency, additivity and the A-null player axiom, and two new axioms called proportionality and strong individual rationality. In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality.