Coalition structure value considering the outside alignment option of priori coalition

Abstract

In a cooperative game with a coalition structure (i.e., coalition structure game), a coalition structure value (CS-value) is obtained on the assumption that the coalition structure has been or can be formed. The necessity analysis of coalition formation is easy to be ignored in the CS-values, such as the Owen value. In this paper, the alignment probability of other coalitions out of a priori coalition is considered as an affection, so that the relative value as a new CS-value is proposed. By different extension of splitting axioms, three kinds of relative values are introduced and axiomatized. These relative values not only take consideration of existing coalition structure, but also other possible coalition structures. Thus, the relative values for a coalition structure in this study are more stable than the Owen value, because the potential affection of other coalition structures is taken into consideration.