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A Game Theory Approach for the Groundwater Pollution Control

Author

Listed:
  • Emmanuelle Augeraud-Véron

    (BSE - Bordeaux Sciences Economiques - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

  • Catherine Choquet

    (ULR - La Rochelle Université)

  • Éloïse Comte

    (UR LISC - Laboratoire d'ingénierie pour les systèmes complexes - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Moussa Diédhiou

    (BSE - Bordeaux Sciences Economiques - UB - Université de Bordeaux - CNRS - Centre National de la Recherche Scientifique)

Abstract

A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temp oral objectives are constrained by a convection-diffusion-reaction equation ruling the spread of the pollution in the aquifer, and the velocity of the flow solves an elliptic partial differential equation. The existence of a Nash equilibrium is proved using a fixed point strategy. A uniqueness result for the Nash equilibrium is also proved under some additional assumptions. Some numerical illustrations are provided.

Suggested Citation

  • Emmanuelle Augeraud-Véron & Catherine Choquet & Éloïse Comte & Moussa Diédhiou, 2022. "A Game Theory Approach for the Groundwater Pollution Control," Post-Print hal-03739654, HAL.
    • Handle: RePEc:hal:journl:hal-03739654
    DOI: 10.1137/19M1278223
    as

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