On weighted-egalitarian values for cooperative games

We propose and characterize weighted-egalitarian values for cooperative transferable utility games. Each weighted-egalitarian value divides the worth of the grand coalition into two parts and allocates them through equality and proportionality based on exogenous player weights. We characterize the family of all weighted-egalitarian values by employing the standard axioms of efficiency and linearity, in addition to two novel axioms: ω-ratio invariance for symmetric players and symmetry in weights. We then show that relaxing linearity to additivity and adding coalitional monotonicity results in a subfamily of affine combinations of equal division and weighted division values. Furthermore, using an axiom called monotonicity in weights, we characterize the family of convex combinations of equal division and weighted division values.