A cooperative game model with bankruptcy theory for water allocation: a case study in China Tarim River Basin.

China Tarim River Basin is located in an arid area, whose rapid socioeconomic development intensifies the current water resources shortage. To allocate water resources reasonably, this paper introduces the bankruptcy theory into the cooperative game model to contract a linear function describing the degree of satisfaction of each region's declared water demand. Bankruptcy theory solves the problem of insufficient information about stakeholders in the cooperative game. From the perspective of the cooperative game's stability, the bankruptcy allocation stability index (BASI) is used to evaluate and compare water resource allocation results in the Tarim River Basin in 2025 and 2030 under different scenarios. Moreover, this paper uses the improved TOPSIS model to build the harmony index of water-economy-environment (HWEE) to evaluate the harmony of water resources, economy, and environment in each region. The results show that the model is more suitable for the actual water allocation game and has a good application value than the classical bankruptcy theory. Moreover, the stability index and HWEE proposed in this paper also have better applicability, and the allocation scheme with the same game weight in each region is more stable.