This paper presents a linear programming model that allocates the waters of the Euphrates and Tigris rivers to irrigation, urban consumption, and on-stream hydroelectricity production in the three riparian countries (Turkey, Syria, and Iraq), by maximizing the aggregate net benefits from water uses while accounting for water-conveyance costs. The model represents, in network form, the system made of the two rivers and their various consumption, supply, and transshipment nodes, and accounts for evaporation and return flows. The constraints include water-conservation balances and maximum and minimum water consumption. The model is used to assess the economic consequences of various cooperation and noncooperation strategies that may be adopted by the riparian countries. Cooperative game-theory concepts (core and Shapley value) are used to identify stable water allocations, under which all three countries find it beneficial to cooperate. The results suggest that an allocation of the total benefits exists, under various scenarios of future energy prices and agricultural productivities, that makes this global cooperation attractive to all countries. Various research extensions are outlined.