Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of stability, has attracted a lot of attention. However, the natural process by which players, starting from any feasible state, strive to reach an equilibrium after a series of unilateral improving deviations, has been less studied. We investigate the convergence of dynamics towards individually stable outcomes under the following perspective: what are the most general classes of preferences and graph topologies guaranteeing convergence? To this aim, on the one hand, we cover a hierarchy of preferences, ranging from the most general to a subcase of additively separable preferences, including individually rational and monotone cases. On the other hand, given that convergence may fail in graphs admitting a cycle even in our most restrictive preference class, we analyze acyclic graph topologies such as trees, paths, and stars.

翻译：图上的联盟形成是一类被广泛研究的博弈，其参与者为图的顶点，且可行联盟必须是连通的子图。在此背景下，各种稳定性概念下均衡的存在性与计算问题已受到大量关注。然而，参与者从任意可行状态出发，经过一系列单边改进偏离以达成均衡的自然过程则研究较少。我们从以下视角研究动态过程向个体稳定结果的收敛性：哪些是最一般的偏好类别与图拓扑结构能够保证收敛？为此，一方面，我们覆盖了从最一般偏好到可加可分偏好子类的偏好层次，包括个体理性与单调偏好情形。另一方面，鉴于即使在限制性最强的偏好类别中，含环图仍可能出现收敛失败，我们分析了无环图拓扑结构，如树、路径和星形图。