Solving Nash Equilibria in Nonlinear Differential Games for Common-Pool Resources
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911531100274688 |
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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 |
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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 |