A Two-Stage Game-Based Model for Decomposition of Water Consumption Control Indicators

Abstract

Water consumption control indicators (WCCI) are key metrics used by China’s water authorities to regulate regional water use, promote conservation, and plan resource utilization. This study proposes a two-stage game-based model for WCCI decomposition across administrative divisions by integrating an improved bankruptcy game and fuzzy cooperative game. In the first stage, the bankruptcy game decomposes WCCI into rigid and non-rigid components to ensure rigid water demand is met, considering regional resources and socio-economic factors. In the second stage, the fuzzy cooperative game enhances water resource benefits by forming cooperation alliances and optimizing non-rigid indicators. The final optimized WCCI is obtained by combining rigid and optimized non-rigid indicators. This method is applied to a case study in HanDan, Hebei Province, China for 2030 under normal (P=50%) and dry (P=75%) year scenarios. The ICEL model achieves 100% water demand satisfaction across all divisions in the normal year, and 80%-98% in the dry year. The fuzzy cooperative game increases overall benefits by 12.9% and 12.7% in the normal and dry years, respectively, with satisfaction rates ranging from 94%-109% in normal and 84%-107% in dry years, optimizing WCCI decomposition.

Keywords: Water Consumption Control Indicators, Rigid Water Demand Assurance, Improved Bankruptcy Game, Fuzzy Cooperative Game, Water Resources Allocation