Additively Separable Hedonic Game (ASHG) are coalition-formation games where we are given a graph whose vertices represent $n$ selfish agents and the weight of each edge $uv$ denotes how much agent $u$ gains (or loses) when she is placed in the same coalition as agent $v$. We revisit the computational complexity of the well-known notion of core stability of ASHGs, where the goal is to construct a partition of the agents into coalitions such that no group of agents would prefer to diverge from the given partition and form a new (blocking) coalition. Since both finding a core stable partition and verifying that a given partition is core stable are intractable problems ($\Sigma_2^p$-complete and coNP-complete respectively) we study their complexity from the point of view of structural parameterized complexity, using standard graph-theoretic parameters, such as treewidth.

翻译：可加可分离享乐博弈（ASHG）是一种联盟形成博弈，其中给定一个图，其顶点表示$n$个自私的智能体，每条边$uv$的权重表示当智能体$u$与智能体$v$被分在同一联盟时，$u$所获（或损失）的收益。我们重新审视ASHG中核稳定性这一经典概念的计算复杂性，其目标在于构造一个智能体的联盟划分，使得不存在任何智能体群体偏好于脱离该划分并形成新的（阻塞）联盟。由于寻找核稳定划分与验证给定划分是否核稳定均为难解问题（分别属于$\Sigma_2^p$-完全和coNP-完全），我们从结构参数化复杂性的角度出发，利用树宽等标准图论参数来研究它们的复杂性。