We present a sufficient condition under which the α-coalitional game associated with a strategic form game is ordinally convex and balanced. The n-person prisoners’ dilemma games satisfy this condition. Copyright Springer-Verlag 2004

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.

The paper deals with the subclass of k-convex n-person transferable utility games which have clear affinities to the well-known convex TU-games. Five new characterizations of a k-convex n-person TU-game are presented in terms of: (1) the unanimity coordinates of TU-game with respect to the...