The Shapley value, one of the well-known allocation rules in game theory, does not take into account information about the structure of the graph, so by using the Shapley value for each hyperedge, we introduce a new allocation rule by considering their first-order combination. We proved that some of the properties that hold for Shapley and Myerson values also hold for our allocation rule. In addition, we found the relationship between our allocation rule and the Forman curvature, which plays an important role in discrete geometry.

翻译：Shapley值作为博弈论中著名的分配规则之一，并未考虑图结构信息。因此，通过将Shapley值应用于每条超边，我们引入了一种基于其一阶组合的新分配规则。我们证明了Shapley值和Myerson值所具有的某些性质在该分配规则下同样成立。此外，我们还发现了该分配规则与Forman曲率之间的关系，后者在离散几何中发挥着重要作用。