of the core of a game on a convex geometry. First, we show that if a game is quasi-convex, then the core is stable. This … result can be seen as an extension of a result by Shapley for traditional cooperative games. Secondly, we show the core on …, we axiomatize the core by means of consistency, as is analogous to a result by Peleg for traditional cooperative games …

Finding a solution concept is one of the central problems in cooperative game theory, and the notion of core is the …, one or several players with all their subordinates. In these situations, the core in its usual formulation may be … unbounded, making its use difficult in practice. We propose a new notion of core, called the restricted core, which imposes …

-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 …

modifications of the Shapley value. We axiomatically characterize these two solutions and study their relation to the strong core …

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 …

interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions called ψ <Superscript …

Let T = (V, E) be a tree. A core of T is a path P, for which the sum of the weighted distances from all vertices to … weights. We prove that, when the sum of the weights of vertices is negative, the core must be a single vertex and that, when … the sum of the vertices’ weights is zero there exists a core that is a vertex. Morgan and Slater (J Algorithms 1 …