Sharing a river among satiable agents

We consider the problem of efficiently sharing water from a river among a group of satiable agents. Since each agent's benefit function exhibits a satiation point, the environment call be described as a cooperative game with externalities. We show that the downstream incremental distribution is the unique distribution which both is fail-according to the "aspiration welfare" principle and satisfies the non-cooperative core lower bounds. On the other hand, the cooperative core may be empty. Furthermore, the downstream incremental distribution satisfies all core lower bounds for all connected coalitions if and only if each agent's individual rationality constraint is independent of the behavior of the other agents. (c) 2007 Elsevier Inc. All rights reserved.