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

Alain Jean-Marie () and M. Tidball
Additional contact information
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

International Game Theory Review (IGTR), 2024, vol. 26, issue 02, 1-21

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.

Keywords: Bio-economic models; Gordon–Schaefer model; singular control (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198924400073
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:26:y:2024:i:02:n:s0219198924400073

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219198924400073

Access Statistics for this article

International Game Theory Review (IGTR) is currently edited by David W K Yeung

More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().