Solving Nash Equilibria in Nonlinear Differential Games for Common-Pool Resources

Fuente: arXiv
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Main Authors: Cai, Yongyang, Xepapadeas, Anastasios, de Zeeuw, Aart
Format: Preprint
Published: 2025
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author Cai, Yongyang
Xepapadeas, Anastasios
de Zeeuw, Aart
author_facet Cai, Yongyang
Xepapadeas, Anastasios
de Zeeuw, Aart
contents Many resources are provided by an ecological system that is vulnerable to tipping when exceeding a certain level of pollution, with a sudden big loss of ecosystem services. An ecological system is usually also a common-pool resource and therefore vulnerable to suboptimal use resulting from non-cooperative behavior. An analysis requires methods to derive cooperative and non-cooperative solutions for managing a dynamical system with tipping points. Such a game is a differential game which has two well-defined non-cooperative solutions, the open-loop and feedback Nash equilibria. This paper provides new numerical methods for deriving open-loop and feedback Nash equilibria, for one-dimensional and two-dimensional dynamical systems. The methods are applied to the lake game, which is the classical example for these types of problems. Especially, two-dimensional feedback Nash equilibria are a novelty of this paper. This Nash equilibrium is close to the cooperative solution which has important policy implications.
format Preprint
id arxiv_https___arxiv_org_abs_2506_06646
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Solving Nash Equilibria in Nonlinear Differential Games for Common-Pool Resources
Cai, Yongyang
Xepapadeas, Anastasios
de Zeeuw, Aart
General Economics
Economics
Many resources are provided by an ecological system that is vulnerable to tipping when exceeding a certain level of pollution, with a sudden big loss of ecosystem services. An ecological system is usually also a common-pool resource and therefore vulnerable to suboptimal use resulting from non-cooperative behavior. An analysis requires methods to derive cooperative and non-cooperative solutions for managing a dynamical system with tipping points. Such a game is a differential game which has two well-defined non-cooperative solutions, the open-loop and feedback Nash equilibria. This paper provides new numerical methods for deriving open-loop and feedback Nash equilibria, for one-dimensional and two-dimensional dynamical systems. The methods are applied to the lake game, which is the classical example for these types of problems. Especially, two-dimensional feedback Nash equilibria are a novelty of this paper. This Nash equilibrium is close to the cooperative solution which has important policy implications.
title Solving Nash Equilibria in Nonlinear Differential Games for Common-Pool Resources
topic General Economics
Economics
url https://arxiv.org/abs/2506.06646