On weighted-egalitarian values for cooperative games with transferable utility

We propose and characterize weighted-egalitarian values for cooperative games with transferable utility. 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, additivity, and continuity, in addition to a novel axiom: weighted ratio invariance for symmetric players. We then show that adding coalitional monotonicity results in a subfamily of affine combinations of equal division value and weighted division values. Furthermore, using an axiom called monotonicity in weights instead of continuity, we characterize the family of convex combinations of equal division value and weighted division values.