DYNAMIC GROUNDWATER RESOURCE MANAGEMENT USING DIFFERENTIAL GAME THEORY AND FINITE DIFFERENCE METHODS: A MULTI-FIRM COMPETITIVE FRAMEWORK

Abstract

The need for groundwater resource sustainability is growing as a result of theeconomic and environmental issues that many areas are facing. In order to examine the dynamics of groundwater extraction, this study created a mathematical model using numer-ical techniques and differential game theory. The model highlights the difficulties caused byresource depletion by using nite difference equations to investigate the relationship betweenextraction rates, groundwater levels, and shadow pricing. When the model was run underrealistic conditions over ten years, the results showed a slow drop in groundwater levelsand a rise in shadow pricing, which ultimately led to lower extraction rates. This studyprovides recommendations for creating sustainable water resource management strategieswhile highlighting the negative eects of groundwater extraction on the environment andthe economy.