Diffusion in dynamic networks with continuous inputs to allocate responsibility

Rosa Van Den Ende () and Dylan Laplace Mermoud ()
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Rosa Van Den Ende: Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Universität Bielefeld, https://centredeconomiesorbonne.cnrs.fr
Dylan Laplace Mermoud: ENSTA, Institut Polytechnique de Paris, Conservatoire National des Arts et Métiers

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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 and practical method to allocate responsibility in real-world networks

Keywords: Dynamic networks; Laplacian matrix; allocation of responsibility; diffusion; climate policy (search for similar items in EconPapers)
JEL-codes: D85 Q5 (search for similar items in EconPapers)
Pages: 29 pages
Date: 2025-04
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