In economic allocation problems, egalitarianism and marginalism are two major thoughts to distribute the benefits of cooperation. The α-CIS value reconciles the two thoughts in some variable extent by a parameter α ∈ [0, 1]. The α-CIS value is the center of gravity of the corresponding α-imputation set given the α-imputation set is nonempty. From the cooperative perspective, we present several axiomatizations of the α-CIS value using α-individual rationality or α-dummifying player property. Finally, we provide a noncooperative interpretation of the α-CIS value by a bidding mechanism.

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