可加可分享乐博弈中强受欢迎性的复杂性
Complexity of Strong Popularity in Additively Separable Hedonic Games
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中文总结 AI 辅助
该研究针对可加可分享乐博弈（ASHGs），证明判定其中强受欢迎划分的存在性为PCW完全问题，解决了相关开放问题，明确了该问题的计算复杂性。
中文摘要 AI 辅助
在享乐博弈中，主体需被划分为联盟，且对划分存在偏好序；若一个划分在主体间的多数投票中击败其他所有划分，则称其为强受欢迎划分。我们聚焦于基础的可加可分享乐博弈（ASHGs），其中主体具有诱导其偏好的可加估值。我们证明，判定ASHGs中强受欢迎划分的存在性是PCW完全问题，PCW是最近提出的、介于$P^{NP}$和$S_2^P$之间的复杂性类（Gilboa等人，2025），这解决了Brandt与Bullinger（2022）以及Bullinger与Gilboa（2025）提出的开放问题。
英文摘要
In a hedonic game, agents need to be partitioned into coalitions, and have a preference order over partitions. A partition is called strongly popular if it beats any other partition in a majority vote among the agents. We focus on the fundamental class of additively separable hedonic games (ASHGs), where agents have additive valuations that induce their preferences. We prove that determining the existence of strongly popular partitions in ASHGs is complete for PCW, a recently introduced complexity class which lies in between $P^{NP}$ and $S_2^P$ (Gilboa et al., 2025). This settles an open problem by Brandt and Bullinger (2022) and Bullinger and Gilboa (2025).
