Fair river sharing is a kind of a fair division problem in which the waters of a river has to be divided among countries located along the river. It differs from other fair division problems in that the resource to be divided—the water—flows in one direction—from upstream countries to downstream countries. To attain any desired division, it may be required to limit the consumption of upstream countries, but this may require to give these countries some monetary compensation.
In addition to sharing river water, which is an economic good, it is often required to share river pollution (or the cost of cleaning it), which is an economic bad.
River sharing in practice
There are 148 rivers in the world flowing through two countries, 30 through three, nine through four and 13 through five or more. Some notable examples are: The Jordan river, whose sources run from upstream Lebanon and Syria to downstream Israel and Jordan. The attempts of Syria to divert the Jordan river, starting in 1965, are cited as one of the reasons for the Six-Day War. Later, in 1994, the Israel–Jordan peace treaty determined a sharing of the waters between Israel and Jordan, by which Jordan receives water per year. The Nile, running from upstream Ethiopia through Sudan to downstream Egypt. There is a long history of disputes over the Nile agreements of 1929 and 1959. The Ganges, running from upstream India to downstream Bangladesh. There was controversy over the operation of the Farakka Barrage. Between Mexico and the United States, there was controversy over the desalination facility in the Morelos Dam. The Mekong runs from China's Yunnan Province to Myanmar, Laos, Thailand, Cambodia, and Vietnam. In 1995, Laos, Thailand, Cambodia, and Vietnam established the Mekong River Commission to assist in the management and coordinated use of the Mekong's resources. In 1996 China and Myanmar became "dialogue partners" of the MRC and the six countries now work together within a cooperative framework.
Property rights
In the international law, there are several conflicting views on the property rights to the river waters. The theory of absolute territorial sovereignty (ATS) states that a country has absolute property rights over any river basin in its territory. So any country may consume some or all of the waters that enter its area, without leaving any water to downstream countries. The theory of unlimited territorial integrity (UTI) states that a country shares the property rights to all the waters from the origin of the river down to its territory. So, a country may not consume all the waters in its territory, since this hurts the right of downstream countries. The theory of territorial integration of all basin states (TIBS) states that a country shares the property rights to all the waters of the river. So each country is entitled to an equal share of the river waters, regardless of its geographic location.
Efficient water allocation
Kilgour and Dinar were the first to suggest a theoretical model for efficient water sharing.
The model
The countries are numbered according to their location, so that country 1 is the most upstream, then 2, etc. The river picks up volume along its course: before each location , an amount of water enters the river. So, country 1 gets water, country 2 gets plus the water unconsumed by country 1, and so on. Each country has a benefit function that describes its utility from each amount of water. This function is increasing but strictly concave function, since the countries have diminishing returns. We can define for each country its marginal benefit function , which describes the price it is willing to pay for an additional unit of water given its current consumption; it is positive but strictly decreasing. Money can be transferred between countries. Countries have quasilinear utility, so a country who consumes water and receives money has utility . A consumption plan is a vector of water allocations and side-payments . The important aspect of the river sharing setting is that water only flows downstream. Therefore, the total consumption at each location must be at most the total amount of water that enters this location: . Additionally, the sum of the side-payments must be at most 0, so that the divider does not have to subsidize the division.
The situation without cooperation
Without cooperation, each country maximizes its individual utility. So if a country is an insatiable agent (its benefit function is always increasing), it will consume all the water that enters its region. This may be inefficient. For example, suppose there are two countries with the following benefit functions: