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Multiple Exploitation of a Renewable Resource — Optimal Solution of a Deterministic Singular Control Model

Author

Listed:
  • Alain Jean-Marie

    (Inria, Montpellier University, 840 Rue Saint Priest, 34000 Montpellier, France)

  • M. Tidball

    (CEE-M, Univ Montpellier, CNRS, INRAE, Institut Agro, 2 Place Viala, 34000 Montpellier, France)

Abstract

In this paper, we consider a singular control optimization problem which generalizes the Gordon–Schaefer model. A population of individuals with endogenous growth is harvested by two independent agents, and their joint profit is maximized. We show that adding a second control to the standard model greatly complicates the standard solution, which is a Most Rapid Approach. We prove that no solution where both controls are singular can exist. Using numerical experiments, we exhibit situations where the optimal steady state corresponds to one of the controls singular, and the other one is equal to one of its specific bounds. In some cases, the optimal path resembles the one-control solution, but with an additional threshold on the population beyond which both controls must be used. However, in other cases, the optimal control has more switching points and is not monotonous. We even exhibit cases where the optimal policy admits two steady states.

Suggested Citation

  • Alain Jean-Marie & M. Tidball, 2024. "Multiple Exploitation of a Renewable Resource — Optimal Solution of a Deterministic Singular Control Model," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 1-21, June.
    • Handle: RePEc:wsi:igtrxx:v:26:y:2024:i:02:n:s0219198924400073
    DOI: 10.1142/S0219198924400073
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