On the extreme points of the core and reduced games

We study the behaviour of the extreme points of the core of a game in front of the reduction of the game and prove that the extreme core points have the reduced game property but not the converse reduced game property. Nevertheless we give some sufficient conditions on an extreme point of the core of a reduced game to extend to an extreme core point of the original game. We introduce the marginal games, which are a special case of reduction, and study some properties, particularlly those related to their extreme core points.