Associated consistency and Shapley value

In this work, a new axiomatization of the Shapley value is presented. An associated game is constructed. We define a sequence of games, when the term of order n, in this sequence, is the associated game of the term of order (n − 1). We show that the sequence converges and that the limit game is inessential. The solution is obtained using the inessential game axiom, the associated consistency axiom and the continuity axiom. As a by-product, we note that neither the additivity nor the efficiency axioms are needed.