2022
DOI: 10.1137/19m1278223
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A Game Theory Approach for the Groundwater Pollution Control

Abstract: A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temporal 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 ar… Show more

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Cited by 2 publications
(2 citation statements)
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“…Kilgour et al ( 1988 ) first used game theory to study the transboundary pollution problem for regulating chemical oxygen demand (COD). Since then, game theory is used by other researchers to analyze the cost/gain effectiveness of pollutant reduction and cost/gain allocations, especially water pollution abatement (Shi et al 2016 ; Augeraud-Véron et al 2022 ). Petrosyan and Yeung ( 2020 ) developed a new class of cooperative dynamic games, which could be used to study the regulation of pollutant emissions.…”
Section: Literature Reviewmentioning
confidence: 99%
“…Kilgour et al ( 1988 ) first used game theory to study the transboundary pollution problem for regulating chemical oxygen demand (COD). Since then, game theory is used by other researchers to analyze the cost/gain effectiveness of pollutant reduction and cost/gain allocations, especially water pollution abatement (Shi et al 2016 ; Augeraud-Véron et al 2022 ). Petrosyan and Yeung ( 2020 ) developed a new class of cooperative dynamic games, which could be used to study the regulation of pollutant emissions.…”
Section: Literature Reviewmentioning
confidence: 99%
“…The user only specifies the date, not the monitoring station, and fuzzy query the monitoring data owned by the specified time point; The user does not specify a date, but only a monitoring station. Fuzzy query is performed on all historical monitoring data of the specified monitoring station [17].…”
Section: System Modulementioning
confidence: 99%