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Cooperative Game for Fish Harvesting and Pollution Control

Author

Listed:
  • Mouhamadou Samsidy Goudiaby

    (Département de Mathématiques, UFR des Sciences et Technologies, Université Assane Seck de Ziguinchor, Ziguinchor BP 523, Senegal)

  • Ben Mansour Dia

    (College of Petroleum Engineering and Geosciences (CPG), King Fahd University of Petroleum and Minerals (KFUPM), Dhahran 31261, Saudi Arabia)

  • Mamadou L. Diagne

    (Département de Mathématiques, UFR des Sciences et Technologies, Université de Thiés, Thiés BP 967, Senegal)

  • Hamidou Tembine

    (Learning & Game Theory Laboratory (L&G-Lab), Division of Engineering, Saadiyat Campus, New York University Abu Dhabi (NYUAD), Abu Dhabi P.O. Box 129188, United Arab Emirates)

Abstract

This paper studies fishery strategies in lakes, seas, and shallow rivers subject to agricultural and industrial pollution. The flowing pollutants are modeled by a nonlinear differential equation in a general manner. The logistic growth model for the fish population is modified to cover the pollution impact on the fish growth rate. We start by presenting the stability analysis of the dynamical system to discern the different types of the evolution of the fish population according to human actions. A cooperative game is formulated to design strategies for preserving the fish population by controlling the pollution as well as the fish stock for harvesting. The sufficient conditions for implementing the cooperative strategy are investigated through an incentive design approach with an adaptive taxation policy for the players. Numerical results are presented to illustrate the benefit of the cooperative for fish population preservation but also for the players’ rewards.

Suggested Citation

  • Mouhamadou Samsidy Goudiaby & Ben Mansour Dia & Mamadou L. Diagne & Hamidou Tembine, 2021. "Cooperative Game for Fish Harvesting and Pollution Control," Games, MDPI, vol. 12(3), pages 1-21, August.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:3:p:65-:d:617659
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    References listed on IDEAS

    as
    1. Olli Tahvonen, 1991. "On the dynamics of renewable resource harvesting and pollution control," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 1(1), pages 97-117, March.
    2. Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    3. Kossioris, G. & Plexousakis, M. & Xepapadeas, A. & de Zeeuw, A. & Mäler, K.-G., 2008. "Feedback Nash equilibria for non-linear differential games in pollution control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1312-1331, April.
    4. Dario Bauso & Ben Mansour Dia & Boualem Djehiche & Hamidou Tembine & Raul Tempone, 2014. "Mean-Field Games for Marriage," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-15, May.
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