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 maximizes the total benefits. To sustain an efficient water allocation, the agents can compensate each other by paying monetary transfers. Every water allocation and transfer schedule yields a welfare distribution, where the utility of an agent is equal to its benefit from the water consumption plus its monetary transfer (which can be negative). The problem of finding a fair welfare distribution can be modelled by a cooperative game.For a river with one spring and increasing benefit functions, Ambec and Sprumont (2002) propose the downstream incremental solution as the unique welfare distribution that is core-stable and satisfies the condition that no agent gets a utility payoff above its aspiration level. Ambec and Ehlers (2008) generalized the Ambec and Sprumont river game to river situations with satiable agents, i.e., the benefit function is decreasing beyond some satiation point. In such situations externalities appear, yielding a cooperative game in partition function form. In this paper we consider river situations with satiable agents and with multiple springs. For this type of river systems we propose the class of so-called weighted hierarchical solutions as the class of solutions satisfying several principles to be taken into account for solving water disputes. When every agent has an increasing benefit function (no externalities) then every weighted hierarchical solution is core-stable. In case of satiation points, it appears that every weighted hierarchical solution is independent of the externalities.
We consider the problem of sharing water among agents located along a river, who have quasi-linear preferences over water and money. The benefit of consuming an amount of water is given by a continuous, concave benefit function. In this setting, a solution efficiently distributes water over the agents and wastes no money. Since we deal with concave benefit functions, it is not always possible to follow the usual approach and define a cooperative river game. Instead, we directly introduce axioms for solutions on the water allocation problem. Besides three basic axioms, we introduce two independence axioms to characterize the downstream incremental solution, introduced by Ambec and Sprumont (2002), and a new solution, called the UTI incremental solution. Both solutions can be implemented by allocating the water optimally among the agents and monetary transfers between the agents.We also consider the particular case in which every agent has a satiation point, constant marginal benefit, equal to one, up to its satiation point and marginal benefit of zero thereafter. This boils down to a water claim problem, where each agent only has a nonnegative claim on water, but no benefit function is specified. In this case, both solutions can be implemented without monetary transfers.
In this paper, we study international river pollution problems. We introduce a model in which countries located along a river from upstream to downstream derive benefits from causing pollution, but also incur environmental costs from experiencing its own pollution and the pollution of all its upstream countries. The total welfare, being the sum of all benefits minus the sum of all costs, is maximized when all countries cooperate. Several principles from international water law are applied to find reasonable and fair distributions of the total welfare that can be obtained under full cooperation. Such a distribution of the welfare at efficient pollution levels can be implemented by monetary compensations.
We consider the problem of sharing water among agents located along a river. Each agent's benefit depends on the amount of water consumed. An allocation of water is efficient when it maximizes total benefits. To sustain an efficient water allocation the agents can compensate each other by monetary transfers. Every water allocation and transfer schedule yields a welfare distribution, where an agent's utility equals its benefit plus (possibly negative) monetary transfer. The problem of finding a fair welfare distribution can be modeled by a cooperative game. We consider river situations with satiable agents and multiple springs. We propose the class of weighted hierarchical solutions, including the downstream incremental solution of Ambec and Sprumont (2002), as a class of solutions satisfying the 'Territorial Integration of all Basin States' principle for sharing water of international rivers. When all agents have increasing benefit functions, every weighted hierarchical solution is core-stable. In case of satiation points, every weighted hierarchical solution is independent of the externalities.
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