New allocation rule of directed hypergraphs

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.