The optimal management of scarce transboundary water resources among competitive users is expected to be challenged by the effects of climate change on water availability. The multiple economic and social implications, including conflicts between neighbouring countries, as well as competitive sectors within each country are difficult to estimate and predict, to inform policy-making. In this paper, this problem is approached as a stochastic multistage dynamic game: we develop and apply a novel framework for assessing and evaluating different international strategies regarding transboundary water resources use, under conditions of hydrological uncertainty. The Omo-Turkana transboundary basin in Africa is used as a case study application, since it increasingly faces the above challenges, including the international tension between Kenya and Ethiopia and each individual country’s multi-sectoral competition for water use. The mathematical framework combines a hydro-economic model (water balance, water costs and benefits), and an econometric model (production functions and water demand curves) which are tested under cooperative and non-cooperative conditions (Stackelberg “leader–follower” game). The results show the cross-country and cross-sectoral water use—economic trade-offs, the future water availability for every game case, the sector-specific production function estimations (including residential, agriculture, energy, mining, tourism sectors), with nonparametric treatment, allowing for technical inefficiency in production and autocorrelated Total Factor Productivity, providing thus a more realistic simulation. Cooperation between the two countries is the most beneficial case for future water availability and economic growth. The study presents a replicable, sophisticated modelling framework, for holistic transboundary water management.