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An explicit solution to harvesting behaviors in a predator–prey system

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  • Guillaume Bataille

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, AMU - Aix Marseille Université, CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper derives closed‐form solutions for a strategic , simultaneous harvesting in a predator–prey system. Using a parametric constraint, it establishes the existence and uniqueness of a linear feedback‐Nash equilibrium involving two specialized fleets and allows for continuous time results for a class of payoffs that have constant elasticity of the marginal utility. These results contribute to the scarce literature on analytically tractable predator–prey models with endogenous harvesting. A discussion based on industry size effects is provided to highlight the role played by biological versus strategic interactions in the multispecies context. Recommendations for Resource Managers This model presents a thorough examination of the economic inefficiencies inherent in the exploitation dynamics of two interdependent species, elucidating the complex interplay between ecological interactions and economic outcomes. The size of the fishing industries constitutes a significant variable that must be integrated into the formulation of pertinent policy recommendations. This constitutes an advancement towards a more time‐consistent approach to Ecosystem‐Based Fishery Management (EBFM).

Suggested Citation

  • Guillaume Bataille, 2024. "An explicit solution to harvesting behaviors in a predator–prey system," Post-Print hal-04793204, HAL.
    • Handle: RePEc:hal:journl:hal-04793204
    DOI: 10.1111/nrm.12408
    Note: View the original document on HAL open archive server: https://hal.science/hal-04793204v1
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    References listed on IDEAS

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    Keywords

    common‐pool resource; dynamic games; fisheries; predator–preyrelationship;
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