  We take an axiomatic approach to the allocation of riparian water rights. We
formalize ethical or structural properties as axioms of allocation rules. We
show that several combinations of these axioms characterize focal rules
implementing the principle of Territorial Integration of all Basin States in
various forms. One of them connects to the Shapley value, the long-standing
centerpiece of cooperative game theory. The others offer natural compromises
between the polar principles of Absolute Territorial Sovereignty and Unlimited
Territorial Integrity. We complete our study with an empirical application to
the allocation of riparian water rights in the Nile River.
