Sharing water resources among cities far from a river basin

This paper considers welfare allocation rules when cities far from a river basin share water resources. The underlying situation is that the cities share a pipe from the water source and they are willing to distribute the welfare produced by using water. I propose two welfare allocation rule: the Shapley value rule and the nucleolus rule. The outcomes of these rules correspond to the Shapley value and the nucleolus, which embody criteria of fairness in the corresponding game respectively. For each rule, I provide an axiomatic characterization under a doctrine called Unlimited Territorial Integrity advocated in international dispute. Moreover, each rule gives a simple expression for computation of the outcome.