Abstract
We investigate hedonic games under enemies aversion and friends appreciation, where every agent
considers other agents as either a friend or an enemy. We extend these simple preferences by allowing each agent to also consider other agents to
be neutral. Neutrals have no impact on her preference, as in a graphical hedonic game. Surprisingly, we discover that neutral agents do not simplify matters, but cause complexity. We prove that
the core can be empty under enemies aversion and
the strict core can be empty under friends appreciation. Furthermore, we show that under both preferences, deciding whether the strict core is nonempty, is NPNP-complete. This complexity extends
to the core under enemies aversion. We also show
that under friends appreciation, we can always find
a core stable coalition structure in polynomial time