We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)s assignment game. We consider the Core, three other notions of group stability and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is...

For each assignment market, an associated bargaining problem is defined and some bargaining solutions to this problem are analyzed. For a particular choice of the disagreement point, the Nash solution and the Kalai-Smorodinsky solution coincide and give the midpoint between the buyers-optimal...

Using a bi-choice graph technique (Klaus and Klijn, 2009), we show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter (Proposition 1). Using this characterization of indirect dominance, we investigate...

Existence of von NeumannMorgenstern solutions (stable sets) is proved for any assignment game. For each optimal matching, a stable set is defined as the union of the core of the game and the core of the subgames that are compatible with this matching. All these stable sets exclude third-party...

We introduce a subclass of multi-sided assignment games that embodies markets with different types of firms that produce different types of homogeneous goods. These markets generalize bilateral Bohm-Bawerk horse markets. We describe the geometric and algebraic structure of the core, which is...

Given an assignment market, we introduce a set of vectors, one for each possible ordering on the player set, which we name the max-payoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn up to...

We provide a different axiomatization of the core interpreted as a reasonable set (Milnor, 1952) and introduce a new property, called max-intersection, related with the vector lattice structure of cooperative games with transferable utility. In particular, it is shown that the core is the only...

We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic...

The main objective of the paper is to study the locus of all core selection and aggregate monotonic point solutions of a TU-game: the aggregate-monotonic core. Furthermore, we characterize the class of games for which the core and the aggregate-monotonic core coincide. Finally, we introduce a...

The core of an assignment market is the translation, by the vector of minimum core payoffs, of the core of another better positioned market, the matrix of which has the properties of being dominant diagonal and doubly dominant diagonal. This new matrix is defined as the canonical form of the...