Axiomatization for the center-of-gravity of imputation set value

In this paper, we introduce the almost inessential game (property) to the solution part of cooperative game theory, which generalizes the inessential game (property). Following the framework of Hamiache to characterize the Shapley value, we then define a new associated game to characterize the center-of-gravity of imputation set value (CIS-value) by means of the almost inessential game property, associated consistency, continuity and efficiency. It provides an interpretation to the CIS-value as the essentially unique fixed point of an endogenous transformation by self-evaluation of TU-games. In addition, symmetry and translation covariance are used to axiomatize the CIS-value instead of the almost inessential property.