  We study the problem of partitioning a set of agents into coalitions based on
the agents' additively separable preferences, which can also be viewed as a
hedonic game. We apply three successively weaker solution concepts, namely
envy-freeness, weakly justified envy-freeness, and justified envy-freeness.
  In a model in which coalitions may have any size, trivial solutions exist for
these concepts, which provides a strong motivation for placing restrictions on
coalition size. In this paper, we require feasible coalitions to have size
three. We study the existence of partitions that are envy-free, weakly
justified envy-free, and justified envy-free, and the computational complexity
of finding such partitions, if they exist.
  We present a comprehensive complexity classification, in terms of the
restrictions placed on the agents' preferences. From this, we identify a
general trend that for the three successively weaker solution concepts,
existence and polynomial-time solvability hold under successively weaker
restrictions.
