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 …

is in the core, it is an extreme point of the core. We first investigate the general relationships between these … over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and … extreme core points. As byproducts, we show that, similarly to the core and the coalitionally rational payoff set, also the …