Page 90 - 2022年第53卷第1期

［ 12］ NAZARI S，AHMADI A，KAMRANI RAD S，et al . Application of non-cooperative dynamic game theory for
groundwater conflict resolution-ScienceDirect［J］. Journal of Environmental Management，2020，270：110889 .
［ 13］ LEE C S . Multi-objective game-theory models for conflict analysis in reservoir watershed management［J］. Che⁃
mosphere，2012，87（6）：608-613 .
［ 14］ NASIRI-GHEIDARI O，MAROFI S，ADABI F . A robust multi-objective bargaining methodology for inter-basin
water resource allocation： a case study［J］ . Environmental Science and Pollution Research，2018，25（3）：
2726-2737 .
［ 15］ CHEN Y，LU H，LI J，et al . A leader-follower-interactive method for regional water resources management with
considering multiple water demands and eco-environmental constraints［J］. Journal of Hydrology， 2017， 548：
121-134 .
［ 16］ SEDGHAMIZ A，NIKOO M R，HEIDARPOUR M，et al . Developing a non-cooperative optimization model for
water and crop area allocation based on leader-follower game［J］. Journal of Hydrology，2018，567：51-59 .
［ 17］ GHORBANI MOOSELU M，NIKOO M R，LATIFI M，et al . A multi-objective optimal allocation of treated waste⁃
water in urban areas using leader-follower game［J］. Journal of Cleaner Production，2020，267：122189 .
［ 18］ ALIZADEH M R， NIKOO M R，RAKHSHANDEHROO G R . Developing a multi-objective conflict-resolution
model for optimal groundwater management based on fallback bargaining models and social choice rules： a case
study［J］. Water Resources Management，2017，31（5）：1457-1472 .
［ 19］ AVISO K B，TAN R R，CULABA A B，et al . Bi-level fuzzy optimization approach for water exchange in eco-in⁃
dustrial parks［J］. Process Safety & Environmental Protection，2010，88（1）：31-40 .
［ 20］ 张鑫，雍志勤，葛杰，等 . 基于区间模糊双层规划的水资源承载力与产业结构优化研究［J］. 水利学报，
2019，50（5）：565-577 .

Non-cooperative game theory method for water resources utilization and pollution control

1
1
FU Xiang 1，2 ，TAN Guangming ，HUANG Sha ，LIU Shuangjun 1，2
（1. State Key Laboratory of Water Resources and Hydropower Engineering Science，Wuhan University，Wuhan 430072，China；
2. Hubei Provincial Key Lab of Water System Science for Sponge City Construction，Wuhan University，Wuhan 430074，China）

Abstract：For ensuring water resources continuous utilization under the priority of water environmental pro⁃
tection，the objective conflicts between economic use of water resources and environmental protection are an⁃
alyzed in this paper. The bargaining games model and leader-followers games model are established for wa⁃
ter resource utilization and pollution control. This paper proposes the coordination method of mutual feed⁃
back decision， and analyses the relationship of Nash equilibrium solution and non-inferior solution. Taking
Four-Inlet river net area of Dongting Lake as study area，the result shows that the equilibrium solutions of
the bargaining games and the leader-followers games method are both at the frontier of the non-inferior so⁃
lution of the multi-objective optimization method. The equilibrium solution range of the bargaining game is
much smaller than non-inferior solution range. Moreover，the leader-followers games model obtains the only
equilibrium solution， which can more effectively control total pollutant discharge. This research provides a
new coordination method for conflict management between water resources utilization and environment protec⁃
tion.
Keywords：economic benefit；total pollutant discharge；bargaining games；leader-followers games；non-infe⁃
rior solution；Nash equilibrium solution

（责任编辑：韩 昆）

— 85 —