『Abstract
　This study applied game theory based models to analyze and solve water conflicts concerning water allocation and nitrogen reduction in the Middle Route of the South-to-North Water Transfer Project in China. The game simulation comprised two levels, including one main game with five players and four sub-games with each containing three sub-players. We used statistical and econometric regression methods to formulate payoff functions of the players, economic valuation methods (EVMs) to transform non-monetary value into economic one, cost-benefit Analysis (CBA) to compare the game outcomes, and scenario analysis to investigate the future uncertainties. The validity of game simulation was evaluated by comparing predictions with observations. The main results proved that cooperation would make the players collectively better off, though some player would face losses. However, players were not willing to cooperate, which would result in a prisoners' dilemma. Scenarios simulation results displayed that players in water scare area could not solve its severe water deficit problem without cooperation with other players even under an optimistic scenario, while the uncertainty of cooperation would come from the main polluters. The results suggest a need to design a mechanism to reduce the risk of losses of those players by a side payment, which provides them with economic incentive to cooperate.

Keywords: Game theory; Water conflicts; Economic valuation; Scenario analysis; The water transfer; China』

1. Introduction
2. Material and methods
　2.1. Area description
　2.2. Data sources
　2.3. Analysis of water quality of the Danjiangkou Reservoir
　2.4. Game-theoretic approach
　2.5. Regression model
　2.6. Transport process of pollutants
　2.7. Total nitrogen reduction
　2.8. Nominal and real values
　2.9. Other methods
　2.10. Scenario design
3. Model
　3.1. Formulating the game model
　　3.1.1. Definition of the players
　　3.1.2. Definition of the strategies
　　3.1.3. Definition of the payoff functions
　3.2. Assumptions
　3.3. Game simulation processes
　3.4. Game solution
　　3.4.1. A non-cooperative game model
　　　3.4.1.1. Water quantity optimization
　　　3.4.1.2. Water quality optimization
　　3.4.2. A cooperative game model
4. Results and discussion
　4.1. Evaluation of game simulation
　4.2. Water deficit
　4.3. nitrogen reduction
　4.4. Payoffs
　4.5. Scenario simulation
5. Conclusions
References
Nomenclature

Fig. 1 . A sketch map of the South-to-North Water Transfer Project. Wei et al.(2010)による『Game theory based models to analyze water conflicts in the Middle Route of the South-to North Water Transfer Project in China』から 南水北調