Carles Rafels

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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 dimension of the core of the assignment game. This result provides an(More)
On the domain of two-sided assignment markets with agents’ reservation values, the nucleolus is axiomatized as the unique solution that satisfies consistency with respect to Owen’s reduced game and symmetry of maximum complaints of the two sides. As an adjunt, we obtain a geometric characterization of the nucleolus by means of a strong form of the bisection(More)
The existence of von Neumann–Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik [11]. For each optimal matching between buyers and sellers, Shubik [12] proposed considering the union of the core of the game and the core of the subgames that are compatible with this matching. We prove in the(More)