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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.

Suggested Citation

  • 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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    1. Flaaten, Ola, 1991. "Bioeconomics of sustainable harvest of competing species," Journal of Environmental Economics and Management, Elsevier, vol. 20(2), pages 163-180, March.
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    3. Fischer, Ronald D. & Mirman, Leonard J., 1996. "The Compleat Fish Wars: Biological and Dynamic Interactions," Journal of Environmental Economics and Management, Elsevier, vol. 30(1), pages 34-42, January.
    4. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    5. David Levhari & Leonard J. Mirman, 1980. "The Great Fish War: An Example Using a Dynamic Cournot-Nash Solution," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 322-334, Spring.
    6. Hannesson, Rognvaldur, 1983. "Optimal harvesting of ecologically interdependent fish species," Journal of Environmental Economics and Management, Elsevier, vol. 10(4), pages 329-345, December.
    7. Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October.
    8. Fischer, Ronald D. & Mirman, Leonard J., 1992. "Strategic dynamic interaction : Fish wars," Journal of Economic Dynamics and Control, Elsevier, vol. 16(2), pages 267-287, April.
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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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