We develop an analytical mathematical framework for groundwater trading among N water producers-consumers connected through a pipe network and regulated by an authority that sets a uniform price. Using a game-theoretic approach, players choose pumping rates to maximise utility by balancing trading profits and pumping costs, leading to a Nash equilibrium. The equilibrium allocation reduces total pumping costs compared to the individualistic scenario and closely approximates the Social Optimum under centralised management, while remaining stable since no rational player has an incentive to deviate. By linking cost reductions to lower energy consumption and groundwater drawdowns, the framework provides a quantitative tool for the efficient regulation of local groundwater markets. We use three examples to illustrate the applicability of the model.
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