Propagation of carbon price shocks through the value chain: the mean-field game of defaults

2025-07-15

AI Summary

This paper examines how carbon pricing propagates through multi-sector value chains and affects investment and production decisions of defaultable firms. Methodologically, it introduces the first mean-field game model in which firm default timing is endogenously determined, integrating endogenous price formation, intersectoral input-output linkages, and CES production technology; firm-level green substitution and exit decisions are formalized via optimal stopping theory. The equilibrium system is reformulated as a tractable linear program, and existence of Nash equilibria and uniqueness of the price system are rigorously established. Numerical experiments demonstrate that rising carbon prices not only stimulate clean technology adoption within individual sectors but also trigger substantial cross-sectoral cascade effects and nonlinear spillovers—highlighting the critical role of intersectoral dependencies in designing effective decarbonization pathways.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

Abstract

We introduce a new mean-field game framework to analyze the impact of carbon pricing in a multi-sector economy with defaultable firms. Each sector produces a homogeneous good, with its price endogenously determined through market clearing. Firms act as price takers and maximize profits by choosing an optimal allocation of inputs-including labor, emissions, and intermediate goods from other sectors-while interacting through the endogenous sectoral price. Firms also choose their default timing to maximize shareholder value. Formally, we model the economy as an optimal stopping mean-field game within each sector. The resulting system of coupled mean-field games admits a linear programming formulation that characterizes Nash equilibria in terms of population measure flows. We prove the existence of a linear programming Nash equilibrium and establish uniqueness of the associated price system. Numerical illustrations are presented for firms with constant elasticity of substitution (CES) production functions. In a stylized single-sector economy, carbon price shocks induce substitution between emissions and labor. In a three-sector economy, the manufacturing sector faces consumer demand and requires inputs from a brown sector, which can be increasingly replaced by green-sector goods as carbon prices rise. These experiments reveal that carbon price shocks can generate substantial spillover effects along the value chain, underscoring the importance of sectoral interdependencies in shaping effective decarbonization pathways.

Problem

• Analyze carbon pricing impact in multi-sector economy with defaults
• Model economy as optimal stopping mean-field game
• Study spillover effects of carbon price shocks across sectors

Innovation

• Mean-field game framework for carbon pricing impact
• Linear programming formulation for Nash equilibria
• CES production functions in multi-sector simulations