We study hedonic games under friends appreciation, where each agent considers other agents friends, enemies, or unknown agents. Although existing work assumed that unknown agents have no impact on an agent’s preference, it may be that her preference depends on the number of unknown agents in her coalition. We extend the existing preference, friends appreciation, by proposing two alternative attitudes toward unknown agents, extraversion and introversion, depending on whether unknown agents have a slightly positive or negative impact on preference. When each agent prefers coalitions with more unknown agents, we show that both core stable outcomes and individually stable outcomes may not exist. We also prove that deciding the existence of the core and the existence of an individual stable coalition structure are respectively NPNP-complete and NP-complete.

In many real-world scenarios, stability is a key property in coalition formation to cope with uncertainty. In this paper, we propose a novel criterion that reshapes stability from robustness aspect. Specifically, we consider the problem of how stability can be maintained even after a small number of players leave the entire game, in the context of hedonic games. While one cannot guarantee the existence of robust outcomes with respect to most of the stability requirements, we identify several classes of friend-oriented and enemy-oriented games for which one can find a desired outcome efficiently. We also show that a symmetric additively hedonic game always admits an outcome that is individually stable and robust with respect to individual rationality.

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 non-empty, is NP^NP-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.