Coalition formation is a central concern in multiagent systems. A common desideratum for coalition structures is stability, defined by the absence of beneficial deviations of single agents. Such deviations require an agent to improve her utility by joining another coalition. On top of that, the feasibility of deviations may also be restricted by demanding consent of agents in the welcoming and/or the abandoned coalition. While most of the literature focuses on deviations constrained by unanimous consent, we also study consent decided by majority vote and introduce two new stability notions that can be seen as local variants of another solution concept called popularity. We investigate stability in additively separable hedonic games by pinpointing boundaries to computational complexity depending on the type of consent and friend-oriented utility restrictions. The latter restrictions shed new light on well-studied classes of games based on the appreciation of friends or the aversion to enemies. Many of our positive results follow from a new combinatorial observation that we call the and that we leverage to prove the convergence of simple and natural single-agent dynamics under fairly general conditions. Our negative results, in particular, resolve the complexity of contractual Nash stability in additively separable hedonic games.

中文翻译：

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加性可分享乐博弈中基于单智能体偏差的稳定性


联盟的形成是多智能体系统中的一个核心问题。联盟结构的一个常见需求是稳定性，其定义是不存在单一主体的有益偏差。这种偏差要求特工通过加入另一个联盟来提高其效用。最重要的是，偏差的可行性也可能受到欢迎和/或放弃联盟中代理人的同意的限制。虽然大多数文献关注的是一致同意所限制的偏差，但我们也研究了多数投票决定的同意，并引入了两个新的稳定性概念，它们可以被视为另一个称为流行度的解决方案概念的局部变体。我们通过根据同意类型和面向朋友的效用限制确定计算复杂性的边界来研究可加分离享乐游戏的稳定性。后者的限制为基于对朋友的欣赏或对敌人的厌恶的经过深入研究的游戏类别提供了新的线索。我们的许多积极结果都来自于我们称之为的新组合观察，我们利用它来证明在相当一般的条件下简单和自然的单智能体动力学的收敛性。特别是，我们的负面结果解决了可加分离享乐博弈中契约纳什稳定性的复杂性。