Enhancing the balance between fairness and efficiency in an inter-basin water allocation plan using a bargaining game theory approach

ABSTRACT Balancing fairness and efficiency in inter-regional water rights allocation remains a major challenge for large-scale water diversion projects. This study proposes a two-stage bargaining framework that integrates a combined weighting approach based on the Order Relation and CRITIC methods with an asymmetric Nash–Harsanyi bargaining model to optimize water rights allocation among the receiving areas of the Hebei section of the South-to-North Water Diversion Project. In the first stage, subjective and objective criterion weights are integrated to determine regional negotiation preferences and initial water claims. In the second stage, an asymmetric bargaining model incorporates regional bargaining power, negotiation breakdown points, and fairness–efficiency considerations to derive the final allocation scheme. A sensitivity analysis of the fairness weighting coefficient was further conducted to evaluate the robustness of the proposed framework. Results indicate that the total regional water claims generated during the first-stage negotiation reached 4.207 billion m3, whereas the bargaining model produced a final optimized allocation of 2.992 billion m3 while guaranteeing 2.525 billion m3 for essential domestic and industrial water demands. Compared with the current allocation scheme, Langfang and Xiong'an New Area receive additional allocations of 94.47 and 160.10 million m3, respectively, whereas regions with relatively lower allocation priorities experience moderate reductions. The sensitivity analysis demonstrates that the proposed framework provides stable allocation results over a reasonable range of fairness weighting coefficients. The proposed methodology offers a transparent and practical decision-support framework for achieving a more balanced regional water rights allocation under competing socio-economic objectives.