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...

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the core of the game. These games will be called buyerseller exact games and satisfy the condition that each mixedpair coalition attains the corresponding matrix...

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the...

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...

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of...

In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequential decision problem. In each step of the process, upper and lower bounds for the payoff of the players are required related to successive...

A new class of games called Financial games is defined. These games are market games and it is showed that they are a generalization of Bankruptcy games. The algebraic structure of this class of games is studied and necessary conditions for a game to be financial are stated. The proportional...

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...

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional...

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...