We study PAC learnability and PAC stabilizability of Hedonic Games (HGs), i.e., efficiently inferring preferences or core-stable partitions from samples. We first expand the known learnability/stabilizability landscape for some of the most prominent HGs classes, providing results for Friends and Enemies Games, Bottom Responsive, and Anonymous HGs. Then, having a broader view in mind, we attempt to shed light on the structural properties leading to learnability/stabilizability, or lack thereof, for specific HGs classes. Along this path, we focus on the fully expressive Hedonic Coalition Nets representation of HGs. We identify two sets of conditions that lead to efficient learnability, and which encompass all of the known positive learnability results. On the side of stability, we reveal that, while the freedom of choosing an ad hoc adversarial distribution is the most obvious hurdle to achieving PAC stability, it is not the only one. First, we show a distribution independent necessary condition for PAC stability. Then, we focus on $\W$-games, where players have individual preferences over other players and evaluate coalitions based on the least preferred member. We prove that these games are PAC stabilizable under the class of bounded distributions, which assign positive probability mass to all coalitions. Finally, we discuss why such a result is not easily extendable to other HGs classes even in this promising scenario. Namely, we establish a purely computational property necessary for achieving PAC stability.

翻译：我们研究了享乐博弈（HGs）的PAC可学习性与PAC可稳定化性，即从样本中高效推断偏好或核心稳定划分的能力。首先，我们扩展了若干最突出HGs类别的已知可学习性与可稳定化性图景，给出了朋友与敌人博弈、底部响应博弈及匿名HGs的结果。随后，着眼于更广阔的视角，我们试图揭示导致特定HGs类别具有或不具有可学习性/可稳定化性的结构特性。在此过程中，我们聚焦于完全表达性的享乐联盟网络表示。我们识别出两组能够实现高效可学习性的条件，这些条件囊括了所有已知的可学习性正向结果。在稳定性方面，我们揭示：虽然选择对抗性分布的自由度是实现PAC稳定性的最明显障碍，但它并非唯一障碍。首先，我们给出一个分布无关的PAC稳定性必要条件。随后，我们关注带权重博弈（$\W$-games）——其中玩家对其他玩家存在个体偏好，并基于最不偏好成员评估联盟。我们证明，在有界分布类（即对所有联盟赋予正概率质量的分布）下，这些博弈是PAC可稳定化的。最后，我们讨论了为何即便在此前景良好的场景下，该结果也难以推广至其他HGs类别：我们建立了实现PAC稳定性所必需的纯计算性质。