  An important aspect in systems of multiple autonomous agents is the
exploitation of synergies via coalition formation. In this paper, we solve
various open problems concerning the computational complexity of stable
partitions in additively separable hedonic games. First, we propose a
polynomial-time algorithm to compute a contractually individually stable
partition. This contrasts with previous results such as the NP-hardness of
computing individually stable or Nash stable partitions. Secondly, we prove
that checking whether the core or the strict core exists is NP-hard in the
strong sense even if the preferences of the players are symmetric. Finally, it
is shown that verifying whether a partition consisting of the grand coalition
is contractually strict core stable or Pareto optimal is coNP-complete.
