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<p>In this paper, we reconsider the sustainable exploitation of a common-pool resource (CPR) problem. It is well-known that without any additional measures, overexploitation or even destruction of a CPR is likely to occur. We investigate three different reward systems for influencing the exploitation of a CPR. As exploitation of a CPR is intrinsically a dynamic problem involving multiple agents and uncertainty, we use a stochastic differential game framework for our study. We extend a model introduced by Jorgensen et al. in this framework with final conditions that model the reward system. We consider a reward if the resource’s stock is above a target level, a tax if it is below, and an unconditional reward depending on the stock at the end of the game. Assuming symmetric play, we consider both the social optimum and Nash equilibrium in this setting. Unfortunately, this extended model does not allow for an analytic solution. Here, we use a local radial basis function scheme combined with the Crank-Nicolson finite difference method to solve the involved partial differential equations. We find that taxing is the most undesirable method of changing and modifying behavior. Furthermore, the results indicate that rewarding players conditionally instead of unconditionally helps to reduce the environmental resource extraction process. A careful balancing of rewarding and taxing is, however, important to achieve this.</p>

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The Impacts of Reward Frequency and Reward Conditionality on Sustainable Use of Common Resources: a Stochastic Common Property Differential Game Model

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Z. Nikooeinejad,
  • M. Heydari,
  • J. Engwerda

摘要

In this paper, we reconsider the sustainable exploitation of a common-pool resource (CPR) problem. It is well-known that without any additional measures, overexploitation or even destruction of a CPR is likely to occur. We investigate three different reward systems for influencing the exploitation of a CPR. As exploitation of a CPR is intrinsically a dynamic problem involving multiple agents and uncertainty, we use a stochastic differential game framework for our study. We extend a model introduced by Jorgensen et al. in this framework with final conditions that model the reward system. We consider a reward if the resource’s stock is above a target level, a tax if it is below, and an unconditional reward depending on the stock at the end of the game. Assuming symmetric play, we consider both the social optimum and Nash equilibrium in this setting. Unfortunately, this extended model does not allow for an analytic solution. Here, we use a local radial basis function scheme combined with the Crank-Nicolson finite difference method to solve the involved partial differential equations. We find that taxing is the most undesirable method of changing and modifying behavior. Furthermore, the results indicate that rewarding players conditionally instead of unconditionally helps to reduce the environmental resource extraction process. A careful balancing of rewarding and taxing is, however, important to achieve this.