Optimal sustainable use of drinking water sources and interactions between multiple providers

The provision and conservation of drinking water are key issues worldwide. Optimal management involves conjunctive use of different sources by multiple providers, who share the same surface water source while using a personal stock source. In this paper we consider the interaction between two profit maximizer providers. We solve two optimal control problems where the optimal abstraction policy of the upstream provider influences the feasible controls of the downstream one. We determine the optimal sustainable policies at every catchment point.