We characterise the welfare implications of uncoordinated policy decisions in the presence of multiple externalities, illustrated with an aquifer. We concentrate on the problem of coordination that can occur when distinct agricultural and water authorities implement their respective policies (to optimise food production and groundwater use) with environmental concerns in mind. We represent this problem as an open-loop Nash game, which compares the game-theoretical solution to a centrally planned solution. We show that the inefficiencies arise from differences in the account taken of relevant costs by different authorities. We demonstrate that the magnitude of the inefficiency generated by the absence of coordination of our authorities varies depending on the weights put on environmental benefits by each authority, and discuss the implications of analysis for future research and policy.