using game theory based approaches to simulate ...

　 　 254 　

2010206 　46 (3)

北京师范大学学报 ( 自然科学版) Jo urnal of Beijing No rmal U niversity (Nat ural Science)

USING GAME THEO RY BASED APPROACHES TO SIM UL ATE STA KEHOLD ER CO NFL ICTS CO NCERNING DOMESTIC WATER ALLOCATIO N AND POLL UTIO N RED UCTIO N IN INTER2BASIN WATER TRANSFER IN CHINA 3 W E I S houke 1 , 2) 　YA N G H on g 1) ( 1) Swiss Federal Instit ute of Aquatic Science and Technology ( EAWA G) , CH28600 , Dü bendorf , Switzerland. 2) Depart ment of Ecosystem and Environmental Informatics , Brandenburg Universit y of Technology , D203046 ,Cott bus , Germany) )

Abstract 　The game t heoretic based simulation app roaches are p ropo sed to analyze conflict s co ncerning do mestic water allocatio n and pollution reduction in t he Middle Route of t he Sout h - No rt h Water Transfer Project in China. Regression met hods are used to fo rmulate payoff f unctions of t he players , eco nomic valuatio n met hods ( EVMs ) to t ransform non2mo netary value into eco no mic o ne , co st2benefit analysis (CBA) to co mpare t he game outcomes , as well as scenario analysis to investigate t he f ut ure uncertainties. The validity of t he game simulatio n was evaluated by co mparing p redictions wit h o bservations. The main result s p roved t hat cooperation would make t he players collectively better off , t ho ugh so me players would face lo sses. It also revealed t hat water pollutio n reductio n wo uld result in a p riso ners ’ dilemma due to unwilling cooperatio n f rom some players. Scenario simulatio n result s displayed t hat water deficit p roblem in t he water scarce area co uld not be solved wit ho ut cooperation even under an optimistic scenario . The application of t ho se app roaches and result s will be info rmative for a st rategic planning on water dist ributio n , water p ricing and ecological co mpensation in t he regio ns co ncerned. Key words 　water conflict s ; game t heo ry ; economic valuation ; scenario analysis ; t he Sout h2Nort h Water Transfer Project in China

( SN W T) Project s , including t he East Ro ute Project ,

0 　Intro duction

t he Middle Ro ute Project and t he West Ro ute

Water scarcit y is o ne of t he vital p ro blems in

Project . However , interbasin water diversio n usually

many co unt ries in t he world. It is estimated t hat

involves different stakeholder s wit h co nt radictory or

today over 2 billio n people are affected by water

co nflicting interest s [ 526 ] , goal s and st rategies [ 3 ] .

shortage in more t han 40 co unt ries in which 11 1 [1 ]

Many eco no mic and political inst rument s have

. Water

been used to solve such co nflict s[ 2 ,7 ] , and water

qualit y degradatio n has beco me o ne of t he main

market app roach is o ne f requently cited in t he

billio n cannot get eno ugh drinking water reaso ns causing water shortage p ro blem

[ 223 ]

. Water

literat ure

[ 8212 ]

. Water market can p rovide water users

diver sio n has been an important measure to alleviate

wit h incentives to use water efficiently , but it

water scarcit y in many co unt ries , especially in China.

requires defining t he original water right s , creating

Due to spatially uneven dist ributio n of p recipitatio n ,

instit utio nal and legal mechanisms , and establishing

water shortage has been a p rolo nged and widesp read

basic inf rast ruct ures for water t rade

p ro blem in t he No rt hern regio n of China

[4 ]

[ 2 ,13 ]

before water

. In order

market can operate well . Waste discharge is a p ublic

to mitigate t he existing water crisis , t he engineer s in

bad , every polluter can f ree2ride ot her s’achievement

China p ropo sed t he So ut h to No rt h Water Transfer

of t reat ment

收稿日期 :2009212216

[ 14 ]

.

Free2riding p ro blem will cause

WEI Shouke , et al : U SIN G GAM E T H EOR Y BASED A PPROAC H ES TO SIMUL A TE STA KE HOLD ER CON FL IC TS CONCERN IN G DOM ESTIC WA TER ALLOCA TION AND POLL U TION 　第 3 期 R EDUC TION IN IN T ER2BASIN WA TER TRANSFER IN C H INA

255 　 　

market failure. In t he absence of market and p ropert y

covers a total area of abo ut 155 000 km2 . The ro ute

multi2stakeholders

cro sses abo ut 200 river channel s or canal s wit h a total

right ,

co nflict s

between

co mpeting for water uses are unavoidable

[ 3 ,15 ]

.

[ 22 ]

lengt h of 1 246 km.

.

Game t heory is an app rop riate app roach to model

Beijing is located in t he nort h2eastern part of

and solve such water co nflict s. A game is a metap hor

China , and it covers an area of 16 808 km ( Fig. 12

of t he ratio nal behavior s of multi2actors in an

b) . It belo ngs to a temperate , semi2humid climate

interacting or interdependent

sit uatio n , such as

do minated mainly by t he Pacific mo nsoo n wit h t ypical

cooperating ,co nflicting ,co mpeting ,coexisting ,etc [ 3 ] .

diver sified nat ure : cold and dry winter , and hot and

In water reso urces management , it was originally

rainy summer , and t he annual average p recipitatio n is

applied in t he co st dist ributio n in joint water reso urce

abo ut 601mm. Due to t he rapid increase in water use

p roject s , i. e. waste water t reat ment and dispo sal

and water pollutio n , water scarcit y is o ne of t he

[ 7 ,16 ]

facilities

.

Lewandowski

[ 17 ]

game2

used a

serio us p ro blems facing t his cit y.

The current

t heoretic app roach to model t he behavio ur of water

available water reso urces per capita is 247 m3 per

user s in a qualit y co nt rol p ro blem , and he p ropo sed a

year , much less t han t he standard for water shortage

game2t heoretic solutio n to different uses of a water

( 1 000 m3 per capita ) defined by t he U nited Natio n

system. Game t heory was used to analyze equitable

( U N ) , and below t he minimum ( 300 m3 per capita )

allocatio n of waste loads to a co mmo n receiving

t hat t he U nited Natio ns Educatio nal , Scientific and

[ 14 ,18224 ]

medium

.

It was also applied into solve

p ro blem in t ransbo undary river pollutio n , including inter2co unt ry river

[6 ]

and int ra2co unt ry river

[ 21 ]

.

Cult ural Organizatio n ( UN ESCO ) defines to ensure a modern social life and production[ 23 ] . The Hanjiang River originates f ro m t he so ut hern

The aim of t his st udy is to establish game

part of Shaanxi p rovince , cro sses t hro ugh Shaanxi

t heoretical simulatio n model s to analyze t he potential

and Hubei p rovinces and joins t he Yangtze River in

water

amo ng

Wuhan. It is t he lo ngest t ributary of t he Yangtze

ho useholds in t he Middle Ro ute of So ut h2to2Nort h

River wit h 1 577 km in lengt h , and t he seco nd largest

qualit y

and

quantit y

co nflict s

sub2basin in

Water Transfer Project in China. The main goals include : 1 ) p redicting do mestic water demand and

water shed area of 159 000 km ( Fig. 12c ) . The river

do mestic water deficit in Beijing , a water scarce areas

flow s t hro ugh subt ropics mo nsoo n area wit h annual

in nort hern China , 2 ) estimating do mestic sewage

p recipitatio n of 873 mm. According to t he data of

discharge in t he upper basin of t he Hanjiang River ,

hydrology series f ro m 1956 —1998 , t he river has total

3 ) evaluating t he eco no mic benefit s and lo sses of

water reso urce of 581 2 billio n m3 and average annual

water diversio n and pollutant reductio n to urban ho useholds in t he st udy area , and 4) analyzing f ut ure

nat ural runoff is 561 6 billio n m3 [ 22 ] . The upper reach of t he river is 925 km lo ng f ro m t he river so urce to

uncertaint y of t he game simulatio n result s using

t he Danjiangko u

different scenario s.

p rovinces of Shaanxi , He’nan and Hubei.

1 　Study are a

Table 1 　De scription of the citie s and

t he

Yangtze

Water Transfer Project s ( M RP ) ( Fig. 12a ) as t he st udy area. The st udy focuses o n t he water qualit y

cit y ,

which

Province

Cit y or Municipalit y

ID

wit h

a

includes part

of

Beijing municipalit y and t he cities in t he upper reach of t he Hanjiang River ( Table 1 ) . The M RP will t ransfer water f ro m t he Danjiangko u Reservoir in t he Basin

to

Beijing

and

Tianjin

Municipalities , Hebei and Henan Provinces , which

Interest Obtaining sufficient water

Beijing (BJ )

Beijing

R1

and quantit y co nflict s amo ng urban ho useholds in

River

basin

their main intere sts in the study

We take t he Middle Ro ute of t he So ut h2to2Nort h

Hanjiang

River 2

for

socio2econo mic

and

environmental p rotection Shaanxi ( SX)

He’nan ( HN) Hubei ( HUB)

Hanzhong

C1

Ankang

C2

Developing

Shangluo

C3

imp roving living standard ,

economy ,

Xixia

C4

reducing pollution based on

Xichuan

C5

t heir economic abilities

Shiyan

C6

　256 　

北京师范大学学报 ( 自然科学版)

第 46 卷 　

Fig. 1 　A sketch map of ( a ) the South2to2North Water Transfer Project , including the We stern Route Project ( WRP) , the Middle Route Project (MRP) and the Ea stern Route Project ( ERP) , (b) Beijing municip ality , and ( c ) the Hanjiang River ba sin

　

　　The Danjiangko u Reservoir , in u2shape , covers

qualit y of water t ransferred to nort h can be well

a water surface area of 1 050 km2 , and has a total

mo nitored.

sto rage capacit y of 171 45 billio n m3 . It owns an average

annual

inflow

of

381 78

billio n

m3 ,

app ro ximately 70 % of water flow of t he entire basin. It is t he water so urce of t he M RP. M RP requires t he water qualit y in t he reservoir meet t he Chinese Surface Water Standard Ⅱ ( GB 3 838 —2002)

[ 24 ]

. In

t his st udy , we selected t hree mo nitoring statio ns in t he

reservoir2Dam ,

Tanzishan

( TZS ) ,

Taocha

( TCA ) wit h numbers 1 , 2 and 3 in Figure 2 — as

The mo nito ring result s show t hat t he annual average co ncent ratio ns of BOD5 ,DO ,CODMn ,N H3 2N meet t he Standard of Class Ⅱ. The co ncent ratio ns of TP in Taocha in 2001 and 2003 were 01 6 mg・ L - 1 and - 1 01 06 mg ・L , which did not meet t he standard of Class Ⅱ ( 01 025 mg ・L - 1 ) , but in ot her year s , t he standard was met ( Fig. 32a ) . However , t he co ncent ratio n of TN belo ngs to Class Ⅳ and V ( Fig. 32b) . The deterioratio n of t ransferable water in t he reservoir is mainly reflected by t he increase in

water qualit y mo nitoring pot s , and t he annual

co ncent ratio n of total nit rogen. Thus , o ur task in t he

average

st udy is to reduce TN co ncent ratio n.

co ncent ratio ns

of

BOD5 , DO , CODMn ,

N H3 2N , TP and TN during 1995 to 2004 as water qualit y indictor s. Tho se t hree statio ns are near t he o utlet of t he so urce of water t ransfer where t he

2 　Data and metho ds 21 1 Data source s This st udy used t hat climatologic

WEI Shouke , et al : U SIN G GAM E T H EOR Y BASED A PPROAC H ES TO SIMUL A TE STA KE HOLD ER CON FL IC TS CONCERN IN G DOM ESTIC WA TER ALLOCA TION AND POLL U TION 　第 3 期 R EDUC TION IN IN T ER2BASIN WA TER TRANSFER IN C H INA

Fig. 2 　Water monitoring stations in the Danjiangkou Re servoir

257 　 　

　

Fig. 3 　Water quality of the Danjiangkou Re servoir in three monitoring stations : Dam , Taizishan and Taocha (a) TP , and (b) TN from 1995 to 2004

sectors.

　

data , hydrolo gical data , water reso urces and water

different

Water

use data , water qualit y data , enviro n2ecological data

pollutant s

as well as socio2eco no mic data , during t he period of

sewage discharge and reclaimed water , etc. Enviro n2

1978 to 2007. The climatologic data mainly include

ecological data include t he data o n urban water

evaporatio n , p recipitatio n and temperat ure.

The

surface areas , p ublic green areas , and t he number s of

main hydrological data are water flow s in different

newly planted t rees , etc. Socio2eco no mic data mainly

mo nitoring statio ns in t he up st ream of t he Hanjiang

include pop ulatio n , co nsumer p rice index , and per

river and t he nat ural inflow of t he Danjiangko u

capita net inco me. We collected t hese data f ro m

reservoir . Water reso urces and water use data refer

mo nitoring statio ns , database of t he Changjiang

to surface water and gro und water , and water use in

Water Reso urce Protectio n Instit ute ( DB2CWRPI) ,

co ncent ratio ns ,

qualit y and

data

urban

include do mestic

　258 　

北京师范大学学报 ( 自然科学版)

第 46 卷 　

o nline statistics database , statistic yearboo ks , official

st udies. The detail of data info rmatio n and data

report s and planning document s as well as p revio us

so urces is summarized in Table 2.

Table 2 　Summary of data and data source s Data

Unit s

Sources

climatological data evaporation

mm

BJ SB. , 2001 —2007 [ 25 ] ; CWRPI. , 2005 [22 ] ; NBSC , 1985 —2007 [26 ] ;

p recipitation

mm

NBSC , 2008 [27 ] ; U N ESCO et al . , 2007 [28 ]

temperat ure

℃

hydrological data 10 8 m3

river flows

8

inflow of Danjiangkou reservior

10 m

CWRPI. , 2005 [22 ] ; Duan , 2003 [ 29 ] .

3

water resources and water use data 10 8 m3

agricult ural water use

BDRC , 2006 [30 ] ; BJ SB. , 2001 —2007 [ 25 ] ; BJ WB. , 2005 [31 ] ;

do mestic water use

8

10 m

3

CWRA . , 1998 —2004 [32 ] ; HRWRC , 1998 —2006 [ 33 ] ; NBSC , 2008 [26 ] ;

ecological water use

8

10 m

3

Wu and Zhang , 2005 [34 ] .

8

3

ground water

10 m

indust rial water use

10 8 m3

overlap amount

10 8 m3

surface water

10 8 m3

water quality data indust rial waste water discharge

BJ SB. , 2001 —2007 [ 25 ] ; CWRPI. , 2005 [22 ] ; HBSB. , 1996 —2005 [35 ] ;

t

pollutant concent ration

mg・ L

- 1

pollutant concent ration t hresholds

mg・ L

- 1

NBSC , 2008 [27 ] ; NBSC and SEPAC , 2000 —2005 [24 ,26 ] ; SEPAC and AQSIQC ,

3

2002 [24 ] ; SXSB. , 1991 —2006 [ 37 ] .

8

reclaimed water

10 m

urban domestic sewage discharge

HNSB , 1994 —2007 [36 ] ;NBSC , 1985 —2007 [26 ] ;

t

environ2ecological data numbers of newly planned t ree

t rees

p ublic green areas

ha

urban water surface areas water quota for public green area water quota for t ree

BJ SB. , 2001 —2007 [ 25 ] ; BJ WCO , 2001 [38 ] ; NBSC , 1985 —2007 [26 ] ; NBSC , 2008 [27 ] .

ha m 3 ・ha - 1 m3 ・ t ree - 1

socio2economic data BJ SB. , 2001 —2007 [ 25 ] ; HB EPB. , 2004 —2005 [ 39 ] ; HBSB. , 1996 —2005 [35 ] ;

consumer p rice index urban per capita net inco me rural and urban pop ulation

yuan

HNSB. , 1994 —2007 [36 ] ; NBSC , 1985 —2007 [26 ] ; SXSB. , 1991 —2006 [ 37 ] .

3

10 person

21 2 　Game theory 　Game t heoretic based app roaches

eco no met ric

are used to simulate do mestic water use co nflict s as

formulate t he payoff f unctio ns of t he players using

games in order to analyze and solve t he p ro blems in t he f ramework of game t heory. A game ( GT ) is usually exp ressed in t he fo rm like equatio n ( 1 ) ,

t he data during 1978 to 1999. The validit y of t he mo dels was evaluated by co mparing p redictio ns wit h o bservatio ns ( data ) during 2000 and 2006. We al so

including Players ( N ) , Actio ns ( A ) , Payoff s ( V ) ,

used eco no mic valuatio n

Informatio n ( I ) , Outco mes ( O ) and Equilibrium

t ransform no n2mo netary values into eco no mic o nes , co st2benefit analysis ( CBA ) to co mpare t he game

regressio n

met hods

met hods

were

used

( EVMs )

to

to

( E) . The simplest game form is a normal form game (o r st rategic game ) ( G) , which can be described as

o utco mes , as well as scenario analysis to investigate

equatio n ( 2 ) , co nsisting of Players ( N ) , St rategy

t he f ut ure uncertainties. Besides , we designed TN

( S ) and Payoff ( V ) .

co ncent ratio n reductio n in t he Danjiangko u Reservoir

GT = { N , A , V , I , O , E} ,

( 1)

G = { N , S , V} ,

( 2)

　　A game modeling and simulatio n p rocess can be simplified as defining a p ro blem as a game , analyzing t he game , setting up game model s , analyzing t he game models and solving t he game

[3 ]

. Statistical and

to follow a linear t rend to reach t he Chinese water qualit y standard of class Ⅱ ( 01 2 mg・ L - 1 ≤TN ≤01 5 mg・ L - 1 ) by 2010. In t he simulatio n p rocess , t he payoff s of t he players are mo netary values calculated based o n current ( or no minal ) p rices. The f ut ure values are

WEI Shouke , et al : U SIN G GAM E T H EOR Y BASED A PPROAC H ES TO SIMUL A TE STA KE HOLD ER CON FL IC TS CONCERN IN G DOM ESTIC WA TER ALLOCA TION AND POLL U TION 　第 3 期 R EDUC TION IN IN T ER2BASIN WA TER TRANSFER IN C H INA

259 　 　

termed as“no minal values”and t he p resent values as

2. 2. 1 　 A non2coo perati ve g ame m odel 　A no n2

“co mparable or real values ”. Co nsumer Price Index ( CPI) is used to kick o ut t he p rice inflatio n and

cooperative game model is developed to analyze t he do mestic water use co nflict s , exp ressed by equatio n

change t he no minal values into co mparable values.

( 3 ) . This model p resent s t hat every player

The no n2cooperative and cooperative mo del s to solve

maximizes t heir

t he p ro blems are p resented in t he following t wo

between benefit s of water usage and t he co st s

sectio ns , and t he notatio ns of all symbol s used in t he

charged to waste reductio n or t reat ment .

net

benefit s , i. e.

i

differences

mo del s are summarized in t he table 3. Table 3 　Summary of the notation de scriptions Main subscript s and superscript s

Q

water use amount (10 8 m3 )

i

every player in a game

Q1

indust rial water demand (10 8 m 3 )

t

a period of time (year in t his st udy)

Q2

do mestic water demand (10 8 m3 )

x

a certain pollutant ( TN in t his st udy)

Q3

agricult ural water demand (10 8 m3 )

y

observed river section

Q4

urban ecological water demand (10 8 m3 )

upper st ream river section

Q5

inst ream base flow demand (10 8 m3 )

p resenting indust ry , household , agricult ure ,

Qg

water demand to keep certain p ublic green area (10 8 m 3 )

urban ecology ,inst ream base flow Input and const rain variables

Qi

water use of player i (10 8 m3 )

Ag

p ublic green areas ( ha)

Qi

minimum water use of player i (10 8 m 3 )

Aw

water surface area ( km2 )

Q gi

maximum water use of player i (10 8 m3 )

B i ( Q)

water benefit f unction player i in non2cooperative game

Qtr

water demand of young t rees (10 8 m3 )

B ( Q)

water benefit f unction in cooperative game

Qw

water demand to keep curtain water surface (10 8 m3 )

cont rolling concent ration of pollutant

Qy

self2p roduced flow in section y (10 8 m3 )

y- 1

1 ,2 ,3 , 4 ,5

ccx , y

x in section y ( mg・ L - 1)

Qy -

pollutant x concent ration in section y ( mg・ L - 1)

cx , y

water flow f rom up st ream (10 8 m3 )

1

reclaimed water (10 8 m3 )

R

pollutant x concent ration in up st ream section ( mg・ L - 1)

T rq

water quota for a t ree ( m3 ・ t ree - 1 )

co st f unction of player i to abate pollutant s in

U

total benefit obtained f ro m cooperative game (10 8 yuan)

non2cooperative game

UB

net benefit obtained f rom cooperative game (10 8 yuan)

co st f unction to abate pollutant s in cooperative game

Ui

payoff of each player i in cooperative game (10 8 yuan)

discount factor

Vi

payoff of every player i (10 8 yuan)

E

water evaporation ( mm)

Wu

ground water (10 8 m 3 )

Gq

water quota of p ublic green area ( m3 ・ha - 1 )

Ws

surface water resources (10 8 m3 )

kx, y

assimilation rate of pollutant x in section y

Wo

overlap bet ween surface and ground water (10 8 m3 )

L cx , y

cont rolling load of pollutant x

W ¨

pollutant s discharge ( TN) (tons)

cx , y -

1

Ci ( W) ¨

C( W) ¨

e - δt

in t he cont rolling section y (tons) L x, y

L x, y -

Pr

1

Greek symbols

load of pollutant of pollutant x

α

coefficient of agricult ure water use

in t he observed section y (tons)

β

benefit coefficient s of water use

load of pollutant x f rom t he up st ream

γ

co st coefficient of reducing pollutant

cont rolling section (tons)

μ

recycling waste water rate

p recipitation ( mm)

ψ

dist ribution factor

n

maxV i = p , d, t

∫ t

[ B i ( Q) - Ci ( W ¨) ]e

- δt

n

dt ,

min Ci ( W ¨) = γx

( 3)

m

∑∑[ ( L

t x , y- 1

+

x =1 y =1

Subject to :

t c L x , y ) (1 - kx , y ) - L x , y ] , n

max B i ( Q) =

∑β Q t i

t =0

t i

,

( 4)

Q1 + Q2 + Q3 ≤ W t

t

t

t S

+W

t u

- W

t O

( 5) t

t

+ R - Q4 , ( 6 )

t t t t t t Q y - 1 + Q y - αQ 3 + μ( Q1 + Q2 ) ≥ Q5 ,

( 7)

　260 　

北京师范大学学报 ( 自然科学版)

( 8)

total payoff in t he no n2cooperatio n and t he total net

( 9)

benefit o btained f ro m cooperatio n , and equatio n ( 21)

( 10 )

means t hat t he total cooperative net benefit sho uld be

Tr T r q ,

( 11 )

not less t han zero , i. e. no net benefit . Ot herwise ,

t i

0 < R < Q ,

( 12 )

cooperatio n will bring lo sses to t he player s.

Q ≤ Q ≤Q g ,

( 13 )

21 3 　 Transport

( 14 )

t ransporting p rocess of do mestic nit rogen into t he

,

( 15 )

reservoir is simplified as fo ur step s : ( 1 ) p ro ducing ,

L x , y = Qy c x , y ,

( 16 )

t

t

t

t

Q4 = Q w + Q g + Qtr , Q

t w

= 10 Q

t g

-5

t

t

= 10

Qtr = 10

-2

-4

t g

t q

A G , t

t i

t i

t i

t x , y- 1

L

= Q

t x, y

t w

( E - Pr ) A ,

t

L

第 46 卷 　

t i

t y- 1

t x , y- 1

c

t y

t x, y

t

c

= Q c

c

,

B , C , Q , V , C ,β, W ¨, L , k , W , E , Pr , A , G, Tr ≥0 , ( 17 )

　 　 In t he co nst rain equatio ns , equatio n ( 4 ) exp resses maximizing eco no mic p roductio n value of using o ne unit of water , and equatio n ( 5 ) states t he co st minimizatio n to reduce o ne unit of a pollutant

pollutant s 　 The

of

( 2 ) entering t he river s , ( 3 ) reaching into t he reservoir , and ( 4 )

nit rificatio n/ denit rificatio n in

reservoir . Part of t he nit rogen will be decayed due to biochemical and ecolo gical p rocesses. This p rocess and t he annual mean co ncent ratio n of nit rogen reached in t he reservoir can

be exp ressed by

equatio ns ( 22) and ( 23) , respectively. Li = W ¨i gλ i i k i