Computational complexity of stable partitions with B-preferences

Consider a special stable partition problem in which the player's preferences over sets to which she could belong are identical with her preferences over the most attractive member of a set and in case of indifference the set of smaller cardinality is preferred. If the preferences of all players over other (individual) players are strict, a strongly stable and a stable partition always exist. However, if ties are present, we show that both the existence problems are NP-complete. These results are very similar to what is known for the stable roommates problem.