Optimizing hydropower generation and sediment transport in Yellow River basin via cooperative game theory

• Streamflow and sediment patterns significantly influence the benefits of cooperative reservoir operation in the YRB. • The three upstream reservoirs Longyangxia, Liujiaxia, and Wanjiazhai contribute most to the grand cooperation. • Shapley value method is recommended to reallocate the incremental benefits of grand cooperation in the YRB. The complicated relationship between water and sediment in the Yellow River Basin (YRB) makes it imperative for reservoir stakeholders to game with each other to balance the short-term and long-term benefits. This paper proposes an integrated model to analyze the cooperation opportunities for major reservoir stakeholders engaged with the Longyangxia, Liujiaxia, Wanjiazhai, Sanmenxia, and Xiaolangdi reservoirs on the YRB mainstream. Multiple benefits are considered, including flood control, water supply, hydropower generation, and sediment trapping. Non-cooperation and cooperation scenarios are compared in this study. The effect of flow and sediment conditions on the incremental benefit of cooperation is examined, which shows that the systematic incremental benefit is larger when the YRB is dryer and sediment concentration is higher. Basin-wide cooperation is especially beneficial when the inflow peak comes earlier and the streamflow process is more fluctuating. Cooperation of reservoir stakeholders in a normal year (2019) can bring more incremental benefit (i.e., $22.57 million) in contrast to the non-cooperation scenario. Longyangxia, Liujiaxia, and Wanjiazhai reservoirs contribute most to the grand cooperation by implementing optimal operation for downstream stakeholders. Three cooperative game theory methods (Shapley value, Gately point, and Nash–Harsanyi solution) are employed to find possible benefit-sharing solutions. Based on cooperative game theory, the results demonstrate the core of basin-wide cooperation in the Yellow River is negligible due to the negative externality effect, implying more measures are needed by the government or non-profit organization to maintain the stability of grand coalition, i.e., water resources utilization control and external compensation. The results also show that Shapley value could be used to reallocate the incremental benefits in the grand cooperation.