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As multiple countries share a river, the likelihood of a water resource conflict from climate change could be higher between countries. In this paper, we demonstrate how countries can cooperate in transboundary water sharing in a sustainable way, given the impacts of climate change. We illustrate the case of water sharing of the Volta River between the upstream and downstream country, Burkina Faso and Ghana respectively, where the latter country faces a tradeoff of water use between agriculture in the north and production of hydro energy in the south. In the framework of a stochastic Stackelberg differential game, we have shown how the issue of water sharing could be linked to hydropower export that can make water sharing between the countries sustaining in the event of climate change. Our results indicate that during cooperation, Ghana will have an opportunity to increase its water abstraction for agriculture, which has remained largely restricted. We also find that the equilibrium strategies in the long run steady state distribution are stable even with increasing variances of water flow.

The paper explores the scope and sustainability of a self-enforcing cooperative agreement in the framework of a game theoretic model, where the upstream and downstream country, Burkina Faso and Ghana respectively in the Volta River Basin, bargain over the level of water abstraction in the upstream. In the model we consider the case where the downstream country, Ghana, offers a discounted price for energy export to the upstream country, Burkina Faso, to restrict its water abstraction rate in the upstream. The paper examines the benefits and sustainability of such self-enforcing cooperative arrangements between Ghana and Burkina Faso given stochastic uncertainty in the river flow. The findings of the paper suggest that at the present condition, the marginal benefit of Burkina Faso from increasing the water abstraction is much higher than that of Ghana's marginal loss. However, the paper finds that if both countries’ water abstraction rates are at a much higher level, then the marginal loss of Ghana increases phenomenally from similar increase in water abstraction rate by Burkina Faso. Under such circumstances, there is an opportunity for Ghana to provide side payments in terms of discounted export price of power in order to motivate Burkina Faso to restrict water abstraction. Die vorliegende Studie untersucht den Rahmen und die Nachhaltigkeit einer selbstbestimmten Kooperationsvereinbarung im Rahmen eines Spieltheorie-Modells, in dem sich die flussauf- bzw. flussabwärts liegenden Länder des Voltabeckens, Burkina Faso und Ghana, über das Maß der Wasserentnahme aus dem oberen Flussbecken verhandeln. In dem Modell wird der Fall betrachtet, in dem das flussabwärts liegende Land, Ghana, dem flussaufwärts gelegenen Burkina Faso einen ermäßigten Energieexportpreis anbietet, um dessen Wasserentnahme einzudämmen. Die Studie untersucht den Nutzen und die Nachhaltigkeit derartiger Vereinbarungen zwischen Ghana und Burkina Faso, wobei zufällige Schwankungen der Abflussmengen berücksichtigt werden. Die Ergebnisse der Studie zeigen, dass unter den gegenwärtigen Voraussetzungen Burkina Fasos Grenzgewinn durch eine erhöhte Wasserentnahme viel höher ist als der dadurch in Ghana zu verzeichnende Grenzverlust. Jedoch wird auch gezeigt, dass im Falle einer bereits höheren Wasserentnahme beider Länder eine weitere Steigerung der Wasserentnahme in Burkina Faso in vergleichbarem Maße zu erheblich höheren Grenzverlusten in Ghana führen würde. Unter solchen Umständen gäbe es für Ghana die Möglichkeit, Anreize in Form reduzierter Energieexportpreise anzubieten, um Burkina Faso zu einer Eindämmung seiner Wasserentnahme anzuregen.