In this paper we present a generalization of the Shapley-Ichiishi result for convex games to the class of all exact games. Then we discuss two applications to the class of convex games. First we show that it can indeed be used to give an alternative proof of the Shapley-Ichiishi result. Secondly...

A set of necessary and sufficient conditions for convexity of a transferable utility game in terms of its decomposition into unanimity games is shown to be minimal: none of the conditions is redundant. The result is used to provide an axiomatization of the Shapley value on the set of convex games.

Total clan games are characterized using monotonicity, veto power of the clan members, and a concavity condition reflecting the decreasing marginal contribution of non-clan members to growing coalitions. This decreasing marginal contribution is incorporated in the notion of a bi-monotonic...