Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this paper, we consider a non-normalized score-based definition of social distance games where the utility function u_v depends on a generic scoring vector v, which may be customized to match the specifics of each individual application scenario. As our main technical contribution, we establish the tractability of computing a welfare-maximizing partitioning of the agents into coalitions on tree-like networks, for every score-based function u_v. We provide more efficient algorithms when dealing with specific choices of u_v or simpler networks, and also extend all of these results to computing coalitions that are Nash stable or individually rational. We view these results as a further strong indication of the usefulness of the proposed score-based utility function: even on very simple networks, the problem of computing a welfare-maximizing partitioning into coalitions remains open for the originally considered canonical function u.

翻译：社交距离博弈作为一种联盟形成模型已被广泛研究，其中每个联盟中代理人的效用通过考虑给定社交网络中距离的效用函数u来刻画。本文考虑基于非归一化分数的社交距离博弈定义，其中效用函数u_v依赖于通用分数向量v，该向量可根据每个具体应用场景的特定需求进行定制。作为主要技术贡献，我们证明了在树状网络结构上，对于任意基于分数的函数u_v，计算代理人社会福利最大化的联盟划分问题是可处理的。我们针对特定u_v选择或更简单网络设计了更高效的算法，并将所有结果扩展到计算纳什稳定或个体理性的联盟。我们认为这些结果进一步有力证明了所提出的基于分数效用函数的实用性：即使在非常简单的网络上，最初考虑的典型函数u所对应的社会福利最大化联盟划分计算问题仍然未解决。