Analysis of Water Resources Allocation Based on Grey Relation-Cooperation Game in Beijing-Tianjin-Hebei Region, China

Water scarcity and water quality degradation in river basins are critical issues addressed by water resources management authorities. Grey relational analysis is adopted to rank key factors affecting water resources in the Beijing-Tianjin-Hebei region. Bankruptcy theory is combined with an improved Nash bargaining game model, and spatiotemporal constraints of cross-regional water resources are incorporated to analyze water allocation under multiple water supply scenarios. Results indicate that the GM (1,1) model achieves Level II (good) prediction accuracy, with relative errors below 6% in most years. The cooperative game model (CGM) yields the highest correlation coefficient of 0.996, indicating the optimal allocation performance. The water demand satisfaction rate in Beijing is the highest among the three regions. An economic compensation range indicator (e) is established for water resource trading games. As the trading water volume increases from 0.01 to 20 billion m3, the feasible compensation range expands from 463.57 to 1,757,045.78 ten thousand yuan. These results provide a scientific basis for rational, stable, and sustainable water resources allocation in the Beijing-Tianjin-Hebei region.