Sharing a river among satiable countries

With diminishing global water reserves the problem of water allocation becomes increasingly important. We consider the problem of efficiently sharing a river among a group of satiable countries. Inducing countries to efficiently cooperate requires monetary compensations via international agreements. We show that cooperation of the other countries exerts a positive externality on the benefit of a coalition. Our problem is to distribute the benefit of efficiently sharing the river under these constraints. If the countries outside of a coalition do not cooperate at all, then the downstream incremental distribution is the unique compromise between the absolute territorial sovereignty (ATS) doctrine and the unlimited territorial integrity (UTI) doctrine. If all countries outside a coalition cooperate, then there may not exist any distribution satisfying the UTI doctrine.