We prove that both the nucleolus and the core-center, i.e., the mass center of the core, of an m-sided Böhm …-Bawerk assignment market can be respectively computed from the nucleolus and the core-center of a convex game defined on the set of m … agents but one need to be taken into account. All these results simplify the computation of the nucleolus and the core …

A solution on a class of TU games that satisfies the axioms of the pre-nucleolus or -kernel except the equal treatment … property and is single valued for two-person games, is a nonsymmetric pre-nucleolus (NSPN) or -kernel (NSPK). We investigate … the NSPKs and NSPNs and their relations to the positive prekernel and to the positive core. It turns out that any NSPK is …

-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals … alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of … weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the …

-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals … alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of … weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the …

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 an assignment game coincides with that of its buyerseller exact …

This note provides two necessary and sufficient conditions for the relative interior of the core (and the base … greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also … imply results on the sensitivity of the base polyhedron and the core. …

The core of an assignment market is the translation, by the vector of minimum core payoffs, of the core of another … analyzed. The kernel and the nucleolus of the assignment game, are proved to be the translation of the kernel and the nucleolus … of the canonical representative by the vector of minimal core payoffs. …