In this paper we consider the problem of sharing water from a river among a group of agents (countries, cities, firms) located along the river. The benefit of each agent depends on the amount of water consumed by the agent. An allocation of the water among the agents is efficient when it...

The Shapley value of a cooperative transferable utility game distributes the dividendof each coalition in the game equally among its members. Given exogenous weightsfor all players, the corresponding weighted Shapley value distributes the dividendsproportionally to their weights. In this...