We initiate the study of control in hedonic games, where an external actor influences coalition formation by adding or deleting agents. We consider three basic control goals (1) enforcing that an agent is not alone (NA); (2) enforcing that a pair of agents is in the same coalition (PA); (3) enforcing that all agents are in the same grand coalition (GR), combined with two control actions: adding agents (AddAg) or deleting agents (DelAg). We analyze these problems for friend-oriented and additive preferences under individual rationality, individual stability, Nash stability, and core stability. We provide a complete computational complexity classification for control in hedonic games.

翻译：我们首次研究了享乐博弈中的操纵问题，其中外部参与者通过添加或删除代理来影响联盟形成。我们考虑三种基本操纵目标：(1) 强制某代理不单独成盟（NA）；(2) 强制一对代理处于同一联盟（PA）；(3) 强制所有代理处于同一大联盟（GR），并结合两种操纵操作：添加代理（AddAg）或删除代理（DelAg）。我们在个体理性、个体稳定性、纳什稳定性和核心稳定性的条件下，针对朋友导向偏好和可加性偏好分析了这些问题。我们为享乐博弈中的操纵问题提供了完整的计算复杂度分类。