A Game Theory Approach for the Groundwater Pollution Control

Emmanuelle Augeraud-Véron, Catherine Choquet, Éloïse Comte () and Moussa Diédhiou
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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

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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.

Keywords: Words; PDEs; Differential game theory; Nash equilibrium; Hydrogeological state equations (search for similar items in EconPapers)
Date: 2022-06
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Published in SIAM Journal on Control and Optimization, 2022, 60 (3), pp.1667-1689. ⟨10.1137/19M1278223⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03739654

DOI: 10.1137/19M1278223

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