The Nile river, which is the longest river in the world, flows from Lake Victoria deep in Africa, which is itself fed by various rivers, through Uganda, Sudan and Egypt until it reaches the Mediterranean sea. On its way it meets the Blue Nile that comes from Ethiopia. The rivers that feed Lake Victoria pass through Zair, Kenya, Tanzania, Rwanda and Burundi. Many countries, they all need water, the needs of the growing populations increase, and one can see that problems are bound to appear. Egypt, the strongest among the countries that use the water of the river is also the most populated one, but it is located downstream: it is the last country to receive its water. Fortunately for the Egyptians, the British who occupied the east of Africa at the beginning of the 20th century wanted to assure the flow of water to Egypt. By an agreement from 1929, 55 billion cubic meter of water out of the 84 billion that flow anually in the river go to Egypt. This agreement was re-affirmed in 1959. Plainly Egypt is happy with this agreement, while the countries that lie upstream are less happy. In fact, these days they try to change the water distribution. This of course maddens Egypt, who unfortunately cannot do much: it lies downstream, so it does not control the flow of the river, and it is far away from the origin of the river: Sudan, whose length from north to south is roughly 2,000 kilometers, separates Egypt from the upstream countries, so Egypt cannot credibly threaten these countries if they decide to use water more than their share according to the 1929 accord. What should be done?

Not surprisingly, game theory does have something to say on this issue. Ambec and Sprumont identify the efficient allocation – the allocation that maximizes the sum of utilities of the various countries; they then present the situation as a cooperative game, find that it is a convex game and therefore has a non-empty core, and further study some properties of this game and its core. There are additional follow-up papers. I did not work out the details to say what Ambec and Sprumont will give to Egypt, but I suspect that it is not applicable. For example, the river flows through Sudan before entering Egypt. Egypt is militarily stronger than Sudan. Egypt may be able to force Sudan into not using the Nile water be credible threats. Egypt, who lies on the mediterranean sea, can desalinate water; this option is not available to Ethiopia, Rwanda and Burundi, who do not have sea-shores, and it will be much more costly to Sudan, whose capital lies far from the red sea. So the game is not a simple game as described by Ambec and Sprumont, but as usual in life it has specific features.

I guess that the nine Nile-river countries will have no choice but to sit together and find a solution that will ensure that all of them have water. Will they? At present Egypt is not ready for that. “Violating Egypt’s quota of Nile water is a genocidal war against 80 million people,” an Egyptian commentator, Hazem el-Beblawi, wrote this year in Al Masry Al Youm, an Egyptian daily <quotation taken from New York Times>. It surprised me to read that Egypt uses this type of rhetoric, the same type of rhetoric that is sometimes used by other strong nations who do not want to cooperate and give up something they unfairly have. But Egypt will have no choice but to cooperate, otherwise it will lose its water.

Back to game theory: can we come up with a model that resembles the Nile river problem more accurately, and takes into account other factors that affect the outcome, and not only the river?