We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas five player game with a unique stable set different from the core,...

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with nonnegative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of...

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal...

Different propietats of convex and average convex games are developed in terms of unanimity coordinates. A set of necessary and sufficient conditions for the core of balanced games containing the Shapley value are given. Connections between convexity and average convexity, the Shapley value, the...

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...