Game theory based models to analyze water conflicts in the Middle Route of the South-to-North Water Transfer Project in China Shouke Wei a,b, *, Hong Yang a,1 , Karim Abbaspour a,1 , Jamshid Mousavi a,c,1 , Albrecht Gnauck b a Department System Analysis, Integrated Assessment and Modelling, the Swiss Federal Institute of Aquatic Science and Technology (EAWAG), Ueberlandstrasse 133, CH-8600 Du ¨ bendorf, Switzerland b Department of Ecosystem and Environmental Informatics, Brandenburg University of Technology, Konrad-Wachsman-Allee 1, D – 03046 Cottbus, Germany c Department of Civil Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran, Iran article info Article history: Received 13 August 2009 Received in revised form 10 December 2009 Accepted 24 January 2010 Available online 1 February 2010 Keywords: Game theory Water conflicts Economic valuation Scenario analysis The water transfer China abstract This study applied game theory based models to analyze and solve water conflicts con- cerning 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 evalu- ated 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 opti- mistic 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 incentives to cooperate. ª 2010 Elsevier Ltd. All rights reserved. 1. Introduction From an economic perspective, water resources are composite assets which provide a variety of services for consumptive and productive activities. However, water quality degradation has been an important cause of water scarcity in countries (Wang et al., 2003; Wei and Gnauck, 2007a). Water resources management on those problems is usually involved with interactive and interdependent stakeholders with contradic- tory or conflicting interests (Fang et al., 1998, 2002; Van der * Corresponding author at: Department System Analysis, Integrated Assessment and Modelling, the Swiss Federal Institute of Aquatic Science and Technology (EAWAG), Ueberlandstrasse 133, CH-8600 Du ¨ bendorf, Switzerland. Tel.: þ41 44 823 5568; fax: þ41 44 823 5375. E-mail addresses: [email protected](S. Wei), [email protected](H. Yang), [email protected](K. Abbaspour), [email protected](J. Mousavi), [email protected](A. Gnauck). 1 Tel.: þ41 44 823 5568; fax: þ41 44 823 5375. Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/watres water research 44 (2010) 2499–2516 0043-1354/$ – see front matter ª 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2010.01.021
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w a t e r r e s e a r c h 4 4 ( 2 0 1 0 ) 2 4 9 9 – 2 5 1 6
Avai lab le a t www.sc iencedi rec t .com
journa l homepage : www.e lsev ie r . com/ loca te /wat res
Game theory based models to analyze water conflicts in theMiddle Route of the South-to-North Water Transfer Projectin China
Shouke Wei a,b,*, Hong Yang a,1, Karim Abbaspour a,1, Jamshid Mousavi a,c,1,Albrecht Gnauck b
a Department System Analysis, Integrated Assessment and Modelling, the Swiss Federal Institute of Aquatic Science and Technology
(EAWAG), Ueberlandstrasse 133, CH-8600 Dubendorf, Switzerlandb Department of Ecosystem and Environmental Informatics, Brandenburg University of Technology, Konrad-Wachsman-Allee 1,
D – 03046 Cottbus, Germanyc Department of Civil Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, Tehran, Iran
a r t i c l e i n f o
Article history:
Received 13 August 2009
Received in revised form
10 December 2009
Accepted 24 January 2010
Available online 1 February 2010
Keywords:
Game theory
Water conflicts
Economic valuation
Scenario analysis
The water transfer
China
* Corresponding author at: Department SystScience and Technology (EAWAG), Ueberlan
1 Tel.: þ41 44 823 5568; fax: þ41 44 823 5370043-1354/$ – see front matter ª 2010 Elsevidoi:10.1016/j.watres.2010.01.021
a b s t r a c t
This study applied game theory based models to analyze and solve water conflicts con-
cerning 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 evalu-
ated 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 opti-
mistic 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 incentives to cooperate.
ª 2010 Elsevier Ltd. All rights reserved.
1. Introduction been an important cause of water scarcity in countries (Wang
From an economic perspective, water resources are composite
assets which provide a variety of services for consumptive and
productive activities. However, water quality degradation has
em Analysis, Integrated Adstrasse 133, CH-8600 Du
(S. Wei), hong.yang@[email protected] (A. Gna5.er Ltd. All rights reserved
et al., 2003; Wei and Gnauck, 2007a). Water resources
management on those problems is usually involved with
interactive and interdependent stakeholders with contradic-
tory or conflicting interests (Fang et al., 1998, 2002; Van der
ssessment and Modelling, the Swiss Federal Institute of Aquaticbendorf, Switzerland. Tel.: þ41 44 823 5568; fax: þ41 44 823 5375.wag.ch (H. Yang), [email protected] (K. Abbaspour),
w a t e r r e s e a r c h 4 4 ( 2 0 1 0 ) 2 4 9 9 – 2 5 1 6 2505
is equal to 1/5 of large animals, 2 goals or sheep, and 30
poultry, respectively, in nitrogen production. Those
researches also stated that the average annual nitrogen
amounts from a person’s manure and liquid, a pig’s manure
and liquid are 1.32 kg a�1, 3.07 kg a�1, 7.58 kg a�1 and
3.93 kg a�1, respectively.
2.7. Total nitrogen reduction
Total nitrogen (TN) concentration reduction in the Danjiang-
kou Reservoir was planned to follow a linear trend to reach the
Chinese water quality standard of Class II (0.2 mg/
L � TN � 0.5 mg/L) by 2010, and the two main reasons for this
consideration are: (1) a straight line is the shortest distance
between two points in geometric and mathematic principle;
(2) a straight line trend to reduce TN means time-cost saving.
The linear trend of upper threshold (Cmax) and lower threshold
(Cmin) of TN concentrations during different years (t), are
expressed by Eqs. (6) and (7).
Cmax ¼ �0:127tþ 255:1 (6)
Cmin ¼ �0:177tþ 355:3 (7)
2.8. Nominal and real values
In the case area, there is a clear time value included in the
benefits and losses of players, because pollution reduction
(cost) will be processed before water transfer (benefit).
Table 3 – Consumer Price Index of Beijing used for the value tr
t CPI t CPI t
1978 100.0 1988 187.6 199
1979 101.8 1989 219.9 199
1980 107.9 1990 231.8 200
1981 109.2 1991 259.4 200
1982 111.2 1992 285.1 200
1983 111.8 1993 339.3 200
1984 114.2 1994 423.8 200
1985 134.4 1995 497.1 200
1986 143.5 1996 554.8 200
1987 155.8 1997 584.2 200
aData from 1978 to 2008 (BJSB, 2001–2009).bValues from 2009 to 2015 are predictions.cThe values in parenthesis from 2006 to 2008 are predictions used to testdThe prediction model is: PI ¼ �6521.67 � 0.79 PI (�2)** þ 1.6 PI (�Prob(F-statistic) < 0.000001, *significant at p <0.01, **significant at p < 0.0
Therefore, the payoff values of the players are not at the same
time level. In details, the benefits of Beijing obtaining from
water diversion will be produced after 2010, while the losses of
the cities in the Hanjiang River basin due to reduction pollu-
tion for water transfer will be generated before 2010. In this
study, we start our pollution reduction from the base 2005,
and we only calculate the benefits of Beijing from 2010 to 2015
in order to compare those 6-year benefits to the 6-year losses.
In this sense, the future values should be discounted and
transformed into the current values. The future values are
termed as ‘‘nominal values’’ and the present values as
‘‘comparable or real values’’. In economics, Consumer Price
Index (CPI) is one of widely used deflator to kick out the price
inflation and change the nominal values into comparable
values. The CPI observation values of Beijing used for the
value discount in this study are listed in Table 3, and the
discount formula can be expressed as:
Dt0
R ¼ DtNpt0
I =ptI (8)
where Dt0R – comparable or real value of payoff (V0 and U0) in
year t0, DtN – nominal value of payoff (V and U ) in year t, pt0
I –
Consumer Price Index in year t0, ptI – Consumer Price Index in
year t.
2.9. Other methods
We used demand-supply principle (DSP), cost-benefit analysis
(CBA) and economic valuation methods (EVMs) to compare the
Fig. 8 – Scenarios (SN) of (a) nitrogen reduction by players 2–4 (P2–P4), (b) nitrogen discharged into the reservoir, by sub-
players 21–23 (P21–P23), (c) nitrogen discharged into the reservoir by sub-players 31–33 (P31–P33), and (d), nitrogen discharged
into the reservoir by sub-players 41–43 (P41–P43).
w a t e r r e s e a r c h 4 4 ( 2 0 1 0 ) 2 4 9 9 – 2 5 1 6 2513
Form those comparing results, it is clear that the players
should cooperate with each other so as to maximize the
overall benefits. However, every player is usually afraid of
cooperation, because they face risks and uncertainties of
losses when they are not sure if others really want to coop-
erate. Furthermore, every player can be better off by free
riding in non-cooperation. In water scarce area, players can
get their water by free riding in terms of overusing ground-
water and ecological water. In the Hanjiang River basin, every
player can also be better off by free riding others’ achievement
of pollution reduction. In a long run, non-cooperation will
deteriorate the environ-ecology and water quality. Therefore,
non-cooperation results in a game of ‘‘Prisoners’ dilemma’’.
The methods to solve the dilemma are usually to design
a mechanism to change the rules and drive the players to
reach collective rationality. The driving forces usually refer to
something like laws, regulations, contracts and other binding
agreement. In contract with those legislation methods,
economic methods such as tax, fine, compensation and so on,
are also such kinds of driving forces. In this study, reducing
waste water and increasing water quality will impose cost to
players in the reservoir catchment, but they can create a large
benefit to the players in water receiving area. In this sense, all
the players will have incentives to cooperate if a mechanism
could guarantee to transfer part of the benefits obtained from
cooperation to cover the losses of players.
4.5. Scenario simulation
The main comparison results from the water demand game
simulation under the four scenarios are illustrated in Fig. 7.
The scenario results revealed that, from 2008 to 2015, water
demand of player 1 (Fig. 7a) will increase under each of those
four scenarios, though the efficiency of water consumption
will be highly increased in those scenarios. Player 1 and his
sub-players would face shortage problems (Fig. 7c and d) in
each of the four scenarios (Fig. 7b), mainly due to increase of
ecological water demand. Comparing to other sub-players,
player 12 will face most serious water deficits in each of the
four scenarios (Fig. 7d). It also found that, due to extremely
severe water scarce situation, those players cannot solve their
water deficits without cooperation with other players, even
under the optimistic scenario 4 (S(4)), where it is in the wet
years (P ¼ 20%), high waste water recycling amount, etc.
The comparing simulation results of TN reduction under
the four scenarios are illustrated in Fig. 8. The results showed
that, in each of the scenarios, player 2 should take more
responsibility to reduce nitrogen production (Fig. 8a), because
he is the main polluter discharging more pollutant TN into the
reservoir than that of other players. The uncertainty of non-
cooperation probably come from this player and his sub-
players because they face big loss to reduce their TN
discharge based on the payoffs results in scenario 1 (Matrix 2).
w a t e r r e s e a r c h 4 4 ( 2 0 1 0 ) 2 4 9 9 – 2 5 1 62514
From the scenario results of sub-games, it is also clear that
sub-players 23, 33 and 43 are the main polluters in games 3, 4
and 5, respectively, because they discharge more nitrogen
than that other players do in each of those gamed under the
four scenarios (Fig. 8c and d).Those sub-players will be the
uncertainty sources of non-cooperation in those games.
5. Conclusions
This study established game-theoretic simulation models to
analyze the problems of water scarcity and nitrogen reduction
in the South-to-North Water Transfer Project. The simulation
is consisted of two levels, 1 main game with 4 players and 4 sub-
games with 12 sub-players. Beijing municipality, Shaanxi
(Hanzhong, Ankang and Shangluo cities), Hubei (Shiyan city)
and He’nan (Xixia and Xichuan cities) were definedas players1,
2, 3 and 4; and industry, household and agriculture of those
four players as the sub-players 11, 12 and 13, 21, 22 and 23, 31, 32
and 33, and 41, 42 and 43, respectively. The main results
revealed that player 1 and its sub-players cannot solve their
water deficit problem without cooperation with other players
even under an optimistic scenario. Sub-player 12 will face most
serious water deficit based on the simulation results of four
scenarios. Cooperation with other players is the dominant
strategy of those players. Players 2–4 and their sub-players will
face costs to reduce pollutant total nitrogen for the water
diversion. The uncertainty of non-cooperation might come
from player 2 in game 1, and sub-players 3 in the games 2–5.
This study also proofed that non-cooperation will cause whole
society a loss although some players can get benefits. In
contract, cooperation brings some players losses, but it will
produce much more collective benefits. However, players
usually are not willing to cooperate, because they will face risks
of losses. This usually results in a game of ‘‘Prisoners’
dilemma’’. The players are willing to cooperate if a mechanism
can guarantee to transfer part of the benefits obtained from
cooperation to cover the losses of players. Suggestions on the
mechanisms can include: (1) to sign a binding agreement on
the beneficial players funding losers to build necessary pollu-
tion treatment plan; (2) to transfer water using and controlling
right to the losing players; and (3) to include the losses of losers
into the water prices for winners. These game simulation
results will not only benefit the water users to be better off, but
also benefit water administration for decision support on water
distribution, water pricing and ecological compensation, etc.
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Nomenclature
A: action (or moves) in a gameB(Q): water benefit function in cooperative gameBi(Q): water benefit function of player i in non-cooperative gameBOD5: biology oxygen demand after 5 days (mg/L)Cra: TN concentration into reservoir from one human activity in
a region (mg/L)C €w;yc : limiting concentration of pollutant (TN) in controlling
section y (mg/L)C €w;y: concentration of pollutant (TN) in the controlling section y
(mg/L)C €w=;y�1: concentration of pollutant (TN) from upstream controlling
section y � 1 (mg/L)CODMn: permanganate index (mg/L)Cmax: upper threshold of TN concentrations (mg/L)Cmin: lower threshold of TN concentrations (mg/L)DN: nominal value of payoff (V and U ) (108 yuan)DR: real value of payoff (V0 and U0) (108 yuan)DO: dissolved oxygen (mg/L)e�dt: discount factorE: game equilibriumEws: evaporation of water surface (mm)GT, G: game, normal form (or strategic)gameG1, G0: first level game, sub-game respectivelyG0m: main player m’s sub-gameI: information set of a gameK(W): cost function to abate pollutant (TN) in cooperative game
(108 yuan)
Ki(W): cost function of player i to abate pollutant in non-cooperative game (108 yuan)
L €w;yc : limiting TN load in section y (tons)Lra: load of TN into the reservoir from one human activity in
a region (mg/L)LW,y: load of pollutant (TN) in section y (tons)LW,y�1: load of pollutant W from upstream controlling section y� 1
(tons)N: set of playersNm, Nmj: set of main players, sub-playersNH3-N: ammonia nitrogen (mg/L)O: game outcomePm, Pmj: main player, sub-playerpt
I ; pt0I ,: consumer price index (CPI) in time t, t0
Qeu: water used for environ-ecology (108 m3)Qf: water inflow into the reservoir (108 m3)Qi,Q 0i : available water of every player in non-cooperative, cooper-
ative game (108 m3)Qed: environ-ecological water demand (108 m3)Qid: water deficit of player i (108 m3)Qi: maximum water demand of player i (108 m3)Qi: minimum water demand of player i (108 m3)Qy�1: water flow from upstream section y � 1 (108 m3)Qy: water flow in the section y (108 m3)Qws: water demand to keep certain water surface (108 m3)Qga: water demand of public green area (108 m3)Qtr: water demand of newly planed trees (108 m3)R: reclaimed water (108 m3)SN: scenariosS: strategy profile of a gameSm,Smj: strategy profile of main player, sub-playerTN: total nitrogen (mg/L)UB: net benefit in cooperative game (108 yuan)Ui, U0i: payoff, real payoff of player i in cooperative game (108 yuan)V: payoff (or utility) in a gameVi, V0i : payoff, real payoff of player i in non-cooperative game
(108 yuan)Vm,Vmj: payoff of main player, sub-player (108 yuan)Wg: groundwater resources (108 m3)Ws: surface water resources (108 m3)Wi, €W
0m: pollutant TN production of player i in non-cooperative,
cooperative game (tons)WiR: pollutant TN reduction of player i (tons)Wra: pollutant TN produced from a certain activity in a region
(tons)Xkp: independent (or explanatory) variablesYp: dependent variablesGreek symbolsa: coefficient of waste water back into waterb: parameter in linear equationb: benefit coefficientg: cost coefficient to reduce pollutant (TN)j: distribution factor of cooperative benefit[: loss coefficient of TN from production sourcel: coefficient of TN into riverk: coefficient of TN into reservoir4: coefficient TN finally maintaining in reservoirh: assimilation coefficient of pollutant3p: disturb (or error) termSubscripts and superscriptsra: one certain human activity in a regionk, p: observation numberst, t0: time (year)i, �i: every player, other n � 1 playerm, j: every main player, sub-player in sub-gamemj: which main player a sub-player belongs toW: referring to pollutant (TN in this study)y, y � 1: lower, upper stream controlling sections