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

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  • Yongyang Cai
  • Anastasios Xepapadeas
  • Aart de Zeeuw

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.

Suggested Citation

  • Yongyang Cai & Anastasios Xepapadeas & Aart de Zeeuw, 2025. "Solving Nash Equilibria in Nonlinear Differential Games for Common-Pool Resources," Papers 2506.06646, arXiv.org.
    • Handle: RePEc:arx:papers:2506.06646
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    File URL: http://arxiv.org/pdf/2506.06646
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