Utilizing the strategic concession behavior in a bargaining game for optimal allocation of water in a transboundary river basin during water bankruptcy

In basins that lie across multiple administrative boundaries, for instance in international river basins like the Nile, water tends to be contested especially during times of scarcity. Riparian countries sharing a transboundary river basin may emphasize the multi-dimensionality of their water demands to obtain access to a greater portion of the available shared water. As a result, the frequency and intensity of water conflicts may increase, hindering the sustainable development of riparian countries and threatening the security and stability of the whole region. Therefore, designing a fair, reasonable, and adaptive allocation scheme is of paramount importance to ensure the integrity of livelihoods and ecosystem health. This paper analyzed the general features of transboundary river basins and built an allocation mechanism combining Bankruptcy Theory with Bargaining and Concession games. A Bankruptcy-Concession-Bargaining Game Model (BCBGM) was constructed to ensure multi-agent participation, multi-stage negotiation, and optimal allocation. Considering the different water demand preferences and linked satisfaction functions, the framework yielded an optimal solution by making concessions on the water claims of riparian countries. As a case study, the proposed model was applied to allocate the limited water resources of the Euphrates-Tigris River. To further measure the stability of model allocation results, a model was built to evaluate the stability of water allocation. The results show that the stability of the allocation output from the proposed allocation framework was relatively high compared to those obtained from classical allocation rules, such as Proportion, Adjusted Proportion, Constrained Equal Loss, and Constrained Equal Award. The model's results satisfied the Pareto efficiency, individual rationality, and maximized group utility. Therefore, for the most part, the allocation outputs of the proposed scheme were generally self-enforceable and sustainable.