[1] Some notable examples are:[2] In the international law, there are several conflicting views on the property rights to the river waters.
[5] Kilgour and Dinar were the first to suggest a theoretical model for efficient water sharing.
So if a country is an insatiable agent (its benefit function is always increasing), it will consume all the water that enters its region.
[6] Because preferences are quasi-linear, an allocation is Pareto-efficient if-and-only-if it maximizes the sum of all agents' benefits and wastes no money.
Under the assumption that benefit functions are strictly concave, there is a unique optimal allocation.
However, this may be impossible because of the structure of the river: the upstream countries do not have access to downstream waters.
, then it is not possible to equalize the marginal benefits, and the optimal allocation is to let each country consume its own water:
The utility of such flexible agreements has been demonstrated by simulations based on historical of the Ganges flow.
[2] Calculating the efficient water allocation is only the first step in solving a river-sharing problem.
The second step is calculating monetary transfers that will incentivize countries to cooperate with the efficient allocation.
According to the ATS doctrine, each country has full rights to the water in its region.
According to the UTI doctrine, each country has rights to all water in its region and upstream.
However, these rights define an upper bound - the largest utility that a country can hope for.
In contrast, if country 2 is satiable (and this fact is common knowledge), then it may be worthwhile for 1 to leave some water to 3, even if some of it will be consumed by 2.
[6] A river carries not only water but also pollutants coming from agricultural, biological and industrial waste.
Evidence from various international rivers shows that, at water quality monitoring stations immediately upstream of international borders, the pollution levels are more than 40% higher than the average levels at control stations.
[10] This may imply that countries do not cooperate for pollution reduction, and the reason for this may be the unclearness in property rights.
Dong, Ni, Wang and Meidan Sun[14]: 3.4 discuss the Baiyang Lake, which was polluted by a tree of 13 counties and townships.
To clean the river and its sources, 13 wastewater treatment plants were built in the region.
The authors discuss different theoretic models for sharing the costs of these buildings among the townships and counties, but mention that at the end the costs were not shared but rather paid by the Baoding municipal government, since the polluters did not have an incentive to pay.
The findings suggest that regional cooperation can be an efficient tool in promoting advanced wastewater treatment, and has several advantages: an efficient use of limited resources (financial and land); balancing disparities between municipalities (size, socio-economic features, consciousness and ability of local leaders); and reducing spillover effects.
Two kinds of licenses are studied: In both markets, free trade can lead to an efficient outcome.
in equilibrium is strictly higher than in the optimal situation, in accordance with the empirical findings of Sigman.
[9] The main question of interest is: how to make countries reduce pollution to its optimal level?
The goal is to find monetary transfers that will make it profitable to agents to cooperate and implement the efficient pollution level.
Gengenbach and Weikard and Ansink[17] focus on the stability of voluntary coalitions of countries, that cooperate for pollution-reduction.
van-der-Laan and Moes[9] focus on property rights and the distribution of the gain in social welfare that arises when countries along an international river switch from no cooperation on pollution levels to full cooperation: It is possible to attain the efficient pollution levels by monetary payments.
The monetary payments depend on property rights: This model can be generalized to rivers that are not linear but have a tree-like topology.
The latter axiom is relevant for non-linear river trees, in which waters from various sources flow into a common lake.
In contrast, the EUR rule might cause a perverse incentive: a country might pay less by polluting more, due to the effect on the estimated transfer rate.