The Extension of Combinatorial Solutions for Cooperative Games

Abstract

In this paper, a new model to solve the social selfish coefficient $\alpha \in \left[ {0,1} \right]$ for the $\alpha$-egalitarian Shapley values and a new convex combinations of single-value in terms of a coalition forming weight coefficient $\beta \in \left[ {0,1} \right]$, which is called the SCE value for cooperative games are presented. The efficiency, linearity, symmetry and $\alpha$-dummy player property of the SCE value are proved. By proposing a procedural interpretation, we define the $\beta$ as the coalition forming weight (or possibility) coefficient and find a new way of assigning the grand coalition profit among all players is coincided with the SCE value which verify the SCE value’s validity, applicability and superiority.