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 …

value, the nucleolus or accountings formulas can be applied and compared. Our analysis is inspired by the need for a …

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. …

(Definition 4.4) and completeness (Definition 4.8). For this class we prove that the core, resp., the nucleolus when the core is … complete Eulerian graphs having the 4-cut property, we are able to test core membership in O(n) time, and when the core is not … empty, we show how to calculate the nucleolus in O(n^2) time, n being the number of players. …

nonredundant core constraints, ease of computation of the core and the nucleolus, and cases of decomposition of the core and the … negative costs on edges and vertices. Among the properties studied are the nonemptiness of the core, characterization of … nucleolus. …

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 buyer–seller exact …

not be balanced. Some conditions for balancedness are provided and, in that case, properties of the core are analyzed … the cores of two assignment games coincides with the core of the sum game. …