Maximizing Social Welfare in Score-Based Social Distance Games

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 $u^s$ depends on a generic scoring vector $s$, 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 $u^s$. We provide more efficient algorithms when dealing with specific choices of $u^s$ 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 $u$.