Abstract: Water saving management contract(WSMC)is a kind of water saving investment model by which water costs saved in the future is used to pay for the cost of project renovation and shared with participants. In order to reasonally address the profit distribution problem of WSMC in the fixed investment and return model, this paper takes initial investment amount, contract period and excess water saving income distribution ratio as research objectives, based on Stackebergs master-slave game theory, four profit distribution models under the non-cooperative game between the water users and the water saving service companies are established; and through numerical examples the optimal equilibrium strategies of the four profit distribution models are analyzed. The results show that the water saving service company and the water users respectively achieve the maximum profit value in the case of the Stackelberg equilibrium when they are in the dominant position. For this water saving renovation project, the economic benefit of the project achieves the maximum profit value when the water saving service company is the leader and the initial investment amount is in a priority decision; at the same time, choosing a water saving service company with higher water saving capacity can produce higher water saving benefits.- DOI:10.3969/j.issn.1000-1565.2023.05.002基于Stackelberg博弈的固定投资回报型合同节水管理收益分配王小胜¹,牛淑月²(1. 河北工程大学 数理科学与工程学院,河北 邯郸 056038;2.河北工程大学 管理工程与商学院,河北 邯郸 056038)摘 要:合同节水管理(water saving management contract,WSMC)是用节约的水费支付项目改造成本并分享节水收益的一种节水投资模式.为了解决固定投资回报型模式下WSMC的收益分配问题,以初始投资额、合同期以及超额节水收益分配比例为研究对象,基于Stackelberg主从博弈理论,建立了用水户和节水服务公司在非合作博弈下的4种收益分配模型,并通过数值算例对4种模式下的最优策略进行分析.结果表明:节水服务公司和用水户分别在其处于主导地位时的Stackelberg均衡下取得最大利润,对于该节水改造项目而言,在节水服务公司主导且优先决策初始投资额的情况下,项目经济效益较好,同时选择较高节水能力的节水服务公司可以产生更高的节水收益.关键词:合同节水管理;固定投资回报型;收益分配;Stackelberg博弈中图分类号:TV213.4 文献标志码:A 文章编号:1000-1565(2023)05-0453-10Profit distribution of water saving management contract in the fixed investment and return model based on Stackelberg gameWANG Xiaosheng¹,NIU Shuyue²(1. School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, China; 2. School of Management Engineering and Business, Hebei University of Engineering, Handan 056038, China)Abstract: Water saving management contract(WSMC)is a kind of water saving investment model by which water costs saved in the future is used to pay for the cost of project renovation and shared with participants. In order to reasonally address the profit distribution problem of WSMC in the fixed investment and return model, this paper takes initial investment amount, contract period and excess water saving income distribution ratio as research objectives, based on Stackebergs master-slave game theory, four profit distribution models under the non-cooperative game between the water users and the water saving service companies are established; and through numerical examples the optimal equilibrium strategies of the four profit distribution models are analyzed. The results show that the water saving service company and the water users respectively achieve the maximum profit value in the case of the Stackelberg equilibrium when they are in the dominant position. For this water saving renovation project, the economic benefit of the project achieves the maximum profit value when the water saving service company is the leader and the initial investment amount is in a priority decision; at the same time, choosing a water saving service company with higher water saving capacity can produce higher water saving benefits.- 收稿日期:2022-08-16 基金项目:国家自然科学基金资助项目(61873084) 第一作者:王小胜(1969—),男,河北邯郸人,河北工程大学教授,博士,主要从事不确定统计预测与决策建模方向研究.E-mail:xswang@hebeu.edu.cn第5期王小胜等:基于Stackelberg博弈的固定投资回报型合同节水管理收益分配

Key words: water saving management contract, fixed investment and return model, profit distribution, Stackelberg game