On extreme points of the core and reduced games

Given a balanced cooperative game, we prove that the extreme points of the core have the reduced game property with respect to the Davis and Maschler reduced game. One particular case of this reduction gives when we name marginal games. These games allow us to define the reduced marginal worth vectors, where every player gets his marginal contribution to a successive marginal game. This set of vectors is proved to be the set of extreme points of the core of those balanced games which are almost convex, that is, those balanced games such that all proper subgames are convex.