Benefit Allocation in Shared Water-Saving Management Contract Projects Based on Modified Expected Shapley Value

Water-Saving Management Contract (WSMC) is an innovative business model to reduce water consumption and improve water-use efficiency. The Shared Water-Saving Model, as a primary operating model in WSMC projects, is relatively widely used compared with other patterns. However, the lack of a water-saving benefit allocation scheme is one of the critical obstacles frustrating the implementation and promotion of the Shared Water-Saving Model. To correct this deficiency, a modified expected Shapley value method is developed, in which alliance revenues are characterized as uncertain variables due to the lack of historical data. Firstly, risk, input and effort are identified as key influencing factors to improve the deficiencies in the distribution of benefits based on the contribution. Secondly, equity criteria, including symmetry, efficiency and additivity, are redefined based on correction factors to measure the fairness of the allocation scheme. Thirdly, we prove that the allocation result obtained by the proposed method satisfies the equity criteria and is unique. Finally, a water-saving project launched by Handan City located in North China is studied to illustrate the applicability of the proposed method. The result shows that the modified expected Shapley value method significantly enhances the cooperative relationship and can therefore be used as an effective tool for the fair and reasonable distribution of benefits in Shared WSMC projects.