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

TL;DR

This paper introduces the edge-based Shapley value, a new allocation rule for networked systems that better captures the contribution of interactions represented by edges, with applications in economic and logistical networks.

Contribution

It develops a novel edge-based Shapley value that shifts from node to edge contributions, establishing its theoretical basis and demonstrating its practical relevance.

Findings

Retains key properties like fairness and symmetry.

Produces intuitive allocations in content platform and supply chain networks.

Handles overlapping routes and cost-sensitive paths effectively.

Abstract

This study introduces the \emph{edge-based Shapley value}, a novel allocation rule within cooperative game theory, specifically tailored for networked systems, where value is generated through interactions represented by edges. Traditional allocation rules, such as the Shapley and Myerson values, evaluate player contributions based on node-level characteristics, or connected components. However, these approaches often fail to adequately capture the functional role of edges, which are crucial in systems such as supply chains and digital platforms, where interactions, rather than individual agents, are the primary drivers of value. 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 the 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. To illustrate its applicability, we present two use cases: content platform networks and supply chain logistics (SCL). In both cases, our method produces intuitive and structurally consistent allocations, particularly in scenarios with overlapping routes, exclusive contracts or cost-sensitive paths. This framework offers a new perspective on value attribution in cooperative settings with complex interaction structures and provides practical tools for analyzing real-world economic and logistical networks.