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arXiv · 2506.06646

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

Yongyang Cai·Anastasios Xepapadeas·Aart de Zeeuw
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Abstract

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.

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Yongyang Cai, Anastasios Xepapadeas, Aart de Zeeuw. 2025-06-07. Solving Nash Equilibria in Nonlinear Differential Games for Common-Pool Resources. https://arxiv.org/abs/2506.06646

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