Efficient water allocation in a transboundary river basin is a complex issue in water resources management. This work develops a framework for the allocation of transboundary river water between the countries located in the river basin to evaluate the characteristics of allocation approaches. The allocation of river water is obtained based on initial-water conditions, cooperative, and non-cooperative game-theoretic approaches. The initial-conditions water allocation approach assigns 34, 40, and 26% of the Harirud River flow to Afghanistan, Iran, and Turkmenistan, respectively. The game-theoretic cooperative approach assigns 36, 42, and 22% of the river flow to Afghanistan, Iran, and Turkmenistan, respectively. The non-cooperative game-theoretic approach establishes that the most stable water allocation was 42, 38, and 20% of the Harirud River flow for Afghanistan, Iran, and Turkmenistan, respectively. Human and agricultural water-stress criteria are used to evaluate the water allocations in the Harirud River basin. The criterion of human water stress has the largest influence in Iran, and the criterion of agricultural water stress has the smallest influence in Afghanistan. This work's results indicate the initial-conditions water allocation approach favors Turkmenistan, whereas the cooperative and the non-cooperative game-theoretic approaches favors Iran and Afghanistan, respectively. The results show that the priorities of each country governs water allocation, and cooperation is shown to be necessary to achieve sustainable development.

Transboundary river basins give rise to complex water-sharing decision making that can be analyzed as a game in the sense of dynamic game theory, as done in this work. The sharing of transboundary water resources depends on the long-term shifting interactions between upstream and downstream countries, which has received limited research attention in the past. The water-sharing strategy of a riparian country depends on the strategies of other countries over time. This paper presents an evolutionary game method to analyze the long-term water-sharing strategies of countries encompassing transboundary river basins over time. The method analyzes the evolutionary strategies of riparian countries and investigates evolutionary stable strategies (ESSs) considering the payoff matrix. The evolutionary game method is applied to a river basin shared by three countries assuming two types of benefits and one type of cost to countries as decision variables of a game that reflects water use, economic and political gains, and socio-economic losses of countries. Numerical examples illustrate the strategies resulting from the evolutionary game processes and the role of several parameters on the interaction between riparian countries. The countries' strategies are analyzed for several levels of benefits and costs, and the convergence of the strategies to a stable point is assessed. Results demonstrate the role that the upstream country's potential benefits and the cost of conflict (i.e., non-cooperation) to other countries has on reaching a stable point in the game. This work's results show the potential benefit to the upstream country under cooperative strategy must exceed its benefits from water use under non-cooperative strategy to gain the full stable cooperation of downstream countries. This work provides a method to resolve water-sharing strategies by countries sharing transboundary river basins and to evaluate the implications of cooperation or non-cooperation.