-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise … parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core …

-298) is proposed to allow for multiple membership. The definition of the core is adapted analogously and the possibilities for …

of ones. We then define the balanced-core as a refinement ofthe core. A payoff vector lies in the balanced-core if it … lies in the core andthe payoff vector is an element of payoff sets of all graphs in some balanced collection ofgraphs. We … prove that any balanced graph game has a nonempty balanced-core.We conclude by some examples showing the usefulness of the …

In this paper, we study different notions of stability for three-sided assignment games. Since the core may be empty in …-Morgenstern stable sets. The dominant diagonal property is necessary for the core to be a stable set, and also sufficient in the case … of the extended cores of all μ-compatible subgames, for a given optimal matching μ, is the core with respect to those …