Diffusion in dynamic networks with time-varying inputs to allocate responsibility

TL;DR

This paper presents a novel dynamic network framework using time-dependent Laplacian matrices to fairly allocate responsibility for indirect impacts in evolving supply chains and interconnected systems.

Contribution

It introduces a responsibility allocation method for dynamic networks that accounts for changing relationships and satisfies key fairness axioms.

Findings

The framework accurately captures responsibility diffusion over time.

Responsibility measures preserve fairness properties when approximated.

Applicable to real-world, evolving supply chain networks.

Abstract

Responsibility in complex networks extends beyond direct actions: players should also bear responsibility for the indirect effects within their supply chains or network. We introduce a novel framework to allocate responsibility for indirect environmental, social, and economic impacts across a dynamic network. Unlike static approaches, our framework accounts for the evolving structure of supply chains, financial systems, and other interconnected systems, where relationships change over time. We use the time-dependent Laplacian matrix to capture how responsibility propagates through the network, revealing a diffusion process that aligns with key axioms of fairness: linearity, efficiency, symmetry, and the independent player property. We show that approximating the responsibility measure preserves these properties, supporting the use of our framework as a rigorous method to allocate responsibility in real-world networks.