Coalition formation studies how to partition a set of agents into disjoint coalitions under consideration of their preferences. We study the classical objective of stability in a variant of additively separable hedonic games where agents can change their valuations. Our objective is to find a stable partition after each change. To minimize the reconfiguration cost, we search for nearby stable coalition structures. Our focus is on stability concepts based on single-agent deviations. We present a detailed picture of the complexity of finding nearby stable coalition structures in additively separable hedonic games, for both symmetric and non-symmetric valuations. Our results show that the problem is NP-complete for Nash stability, individual stability, contractual Nash stability, and contractual individual stability. We complement these results by presenting polynomial-time algorithms for contractual Nash stability and contractual individual stability under restricted symmetric valuations. Finally, we show that these algorithms guarantee a bounded average distance over long sequences of updates.

翻译：联盟形成研究如何在考虑智能体偏好的情况下，将一组智能体划分为互不相交的联盟。我们在可加可分离的享乐博弈的一个变体中研究经典的稳定性目标，其中智能体可以改变其估值。我们的目标是在每次变化后找到一个稳定的划分。为了最小化重构成本，我们搜索邻近的稳定联盟结构。我们的重点是基于单智能体偏离的稳定性概念。我们针对可加可分离享乐博弈中寻找邻近稳定联盟结构的复杂性，在对称与非对称估值两种情形下，给出了详细的图景。我们的结果表明，对于纳什稳定性、个体稳定性、契约纳什稳定性以及契约个体稳定性，该问题均是NP完全的。我们通过提出在受限对称估值下针对契约纳什稳定性与契约个体稳定性的多项式时间算法，对这些结果进行了补充。最后，我们证明这些算法能够保证在长更新序列上的平均距离有界。