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 …

: (i) only eight configurations are possible for the core, which contains at most six allocations; (ii) for each core …