New allocation rule based on graph structures and their application to economic phenomena

Abstract

This study introduces an edge-based Shapley value, a novel allocation rule in cooperative game theory tailored specifically to supply chain networks, where value is generated through edge-mediated interactions.Traditional allocation rules, such as the Shapley value and Myerson value, evaluate player contributions based on node-level characteristics or connected components.However, these approaches often fail to adequately capture the functional role of edges that represent supply routes with associated costs and flow volumes. Our edge-based Shapley value shifts the characteristic function from node sets to edge sets, thereby enabling a more granular and context-sensitive evaluation of supplier contributions. We establish its theoretical foundations, demonstrate its relationship to classical allocation rules, and show that it retains key properties such as fairness and symmetry. We apply the method to supply chain networks by incorporating route-specific supply quantities and transportation costs via a cost-decaying weight function, and validate the approach through a systematic empirical benchmark on seven distinct supply network topologies, spanning serial, parallel-redundant, asymmetric tier, scale-free, clustered, layered DAG, and single-point-of-failure structures. Furthermore, we show that ESV rankings are more robust to prior network disruption than the single-node removal measure: when portions of the network have already failed, the ESV computed on the original intact network predicts the remaining nodes' importance more accurately than the single-node removal measure, because the Shapley value inherently averages over all possible degradation states.