Optimal policies for environmental assets under spatial heterogeneity and global awareness

2025-10-24

AI Summary

This paper addresses the optimal management of environmental assets in geospatial settings under non-cooperative governance: local policymakers maximize regional welfare, which depends on both local and global environmental states, inducing strategic interdependence. Methodologically, it integrates spatial heterogeneity and global externalities into a unified stochastic differential game framework. It derives, for the first time, open-loop and closed-loop Nash equilibria for an N-player game and rigorously establishes their convergence to a mean-field equilibrium. Explicit analytical solutions are obtained for all equilibria and the socially optimal benchmark, enabling precise quantification of efficiency losses from non-cooperation. Building on this, the paper designs a spatially differentiated Pigouvian tax mechanism that asymptotically aligns decentralized decisions with the social optimum. The approach synthesizes stochastic control, differential game theory, and mean-field game analysis, providing a rigorous theoretical foundation and actionable policy instruments for transboundary environmental governance.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The aim of this paper is to formulate and study a stochastic model for the management of environmental assets in a geographical context where in each place the local authorities take their policy decisions maximizing their own welfare, hence not cooperating each other. A key feature of our model is that the welfare depends not only on the local environmental asset, but also on the global one, making the problem much more interesting but technically much more complex to study, since strategic interaction among players arise. We study the problem first from the $N$-players game perspective and find open and closed loop Nash equilibria in explicit form. We also study the convergence of the $N$-players game (when $n o +infty$) to a suitable Mean Field Game whose unique equilibrium is exactly the limit of both the open and closed loop Nash equilibria found above, hence supporting their meaning for the game. Then we solve explicitly the problem from the cooperative perspective of the social planner and compare its solution to the equilibria of the $N$-players game. Moreover we find the Pigouvian tax which aligns the decentralized closed loop equilibrium to the social optimum.

Problem

• Managing environmental assets with non-cooperative local authorities
• Studying strategic interactions in welfare-dependent global environmental systems
• Finding Nash equilibria and Pigouvian taxes for decentralized optimization

Innovation

• Stochastic model for environmental asset management
• Nash equilibria in N-player and mean field games
• Pigouvian tax aligning decentralized equilibrium to optimum