A two-stage game-based model for distribution of water consumption control indicators

Handan, China. 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 integrates an improved bankruptcy game model with a fuzzy cooperative game model to propose a two-stage decomposition method. In the first stage, the bankruptcy game model divides WCCI into rigid and non-rigid indicators, ensuring rigid water demand is met while considering regional resources and socio-economic factors. In the second stage, the fuzzy cooperative game model optimizes non-rigid indicator distribution by forming water resource cooperation alliances, enhancing overall benefits. A case study in Handan, Hebei Province, China, was conducted using the “city-county” administrative division approach. WCCI decomposition was analyzed under two water availability scenarios in 2030: normal years (P = 50 %) and dry years (P = 75 %). Results show that under the bankruptcy game model, water demand satisfaction reaches 100 % in normal years and 80 %-98 % in dry years. Under the fuzzy cooperative game model, overall benefits increase by 12.9 % in normal years and 12.7 % in dry years, with water demand satisfaction ranging from 94 % to 109 % in normal years and 84 %-107 % in dry years. This method offers a new perspective on optimal water resource allocation, improving efficiency and fairness. • The WCCI distribution framework based on bankruptcy and fuzzy cooperative game. • Basic water demands of all users are addressed to ensure their water security. • Incorporates hydraulic connections to optimize regional water benefits via game theory.