A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces aij units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core...

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...

The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik (1972) [11]. For each optimal matching between buyers and sellers, Shubik (1984) [12] proposed considering the union of the core of the game and the core...

In the framework of bilateral assignment games, we study the set of matrices associated with assignment markets with the same core. We state conditions on matrix entries that ensure that the related assignment games have the same core. We prove that the set of matrices leading to the same core...

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...

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...

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...

To any assignment market we associate the unique exact assignment game defined on the same set of agents and with a core that is a translation of the core of the initial market. As it happens with the core, the kernel and the nucleolus of an assignment game are proved to be the translation of...

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...