The Shapley value for cooperative games with restricted worths

Abstract

In this paper, we define the cooperative games with restricted worths, which is based on the coalition structure. The model describes many cooperative situations in modern society. The Shapley value is investigated under this model and we reveal the relations with other coalitional values. Furthermore, two new axioms are proposed to characterize the Shapley value, namely the coalitional-individual marginality and the coalitional-individual symmetry.