We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming edges from outside the coalition. The resulting game has a convenient representation in terms of unanimity games. This representation enables closed-form polynomial-time formulas for the Shapley and Banzhaf values. We further establish that the game has a nonempty core and is totally balanced. The class of such games therefore provides an analytically and computationally tractable example of structured network- induced cooperative games in which stability-based allocations and fairness-based solution concepts do not coincide.

翻译：我们引入了一类由加权有向图诱导的合作博弈。具体而言，联盟值结合了由诱导子图博弈给出的内部交互项，以及基于联盟外部最小入边的外部分量。由此产生的博弈具有基于一致博弈的简洁表示。该表示使得沙普利值和班扎夫值能够通过闭式多项式时间公式计算。我们进一步证明了该博弈具有非空核且是完全平衡的。因此，这类博弈提供了分析上和计算上可处理的结构化网络诱导合作博弈的范例，其中基于稳定性的分配方案与基于公平性的解概念并不一致。