Three characterizations of the weighted center of imputations value

The weighted center of imputations (CIS) value allocates the surplus of the grand coalition equally after granting each player a fixed proportion of his individual worth. This paper provides three axiomatic characterizations of this value by generalizing the individual rationality and subgame order preservation axioms. The first characterization employs individual rationality with respect to the weights together with the equal surplus increment property. The second relies on efficiency, additivity, symmetry adjusted by the weights, and a dummifying player property adapted to the weights. The third builds on efficiency and a weak subgame order preservation axiom that incorporates the weights. These results unify and extend recent findings, covering both the equal division and the standard CIS values as special cases.