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An Explicit Solution to Harvesting Behaviors in a Predator-Prey System

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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 allow for continuous time results for a class of payoffs that have constant elasticity of the marginal utility. Theses 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 multi-species context.

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  • Guillaume Bataille, 2024. "An Explicit Solution to Harvesting Behaviors in a Predator-Prey System," AMSE Working Papers 2405, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:2405
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    References listed on IDEAS

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    More about this item

    Keywords

    fisheries; Dynamic games; common-pool resource; Predator-prey relationship;
    All these keywords.

    JEL classification:

    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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