Anik Bhaduri1, Utpal Manna2, Edward Barbier3 and Jens
Liebe1
1.Center for Development Research, University of Bonn, Germany
2.Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
3. University of Wyoming,USA
EAERE 2009 Amsterdam
Climate Change and Water Conflict
 IPCC Report (2008): The impact of Global climate
change on water resources could be significant.
 Uncertainty in rainfall, and in the availability of water
could lead to an increase in demand for irrigation of
surface water.
 Conflict could be outcome (Stern Report).
 In a transboundary setting, where multiple countries
share a river, conflict could be much higher.
Coperation and Conflict are the
two sides of the same coin........
 Cooperation has consistently dominated water
relating conflicts in the past.
 However, there are cases where there is limited scope
of cooperation.
 Even under conditions of limited scope of cooperation,
there is a possibility of attaining agreement, through
linking to issues of mutual interest to the parties.
The Volta Basin:
5%
42%
4%
6%
3%
40%
• 400,000 km2
• 6 riparian countries
• 20+ million inhabitants
+
Expansion
of irrigated
Major
Challenge
in the Volta
Basin foragriculture
Water Resources
Management
Hydropower generation
at Akosombo
Irrigation Development in Burkina
Faso and Ghana
Expansion
of irrigated
Major
Challenge
in the Volta
Basin foragriculture
Water Resources
Management
Hydropower generation
at Akosombo
Expansion
of irrigated
Major
Challenge
in the Volta
Basin foragriculture
Water Resources
Management
Hydropower generation
at Akosombo
Objective
 Scope of sharing of river given the uncertainty of the
water resources.
 Issue linkage to water sharing could be hydropower
export from Ghana to Burkina Faso.
 Sustainability of cooperation under climate change
issue.
Structure
 A stochastic differential Stackelberg leader-follower
game in a setting where Ghana offers a discounted
price for energy export to the upstream country,
Burkina Faso, for more water in the downstream.
 Compare both the cooperative as well as non
cooperative outcomes in a possible climate change
scenario.
Lit review
 Fisher and Rubio(et. al. 1997)
Tsur and Graham Tomasi 1991.
 Knapp and Olson (1995)
 Chatterjee , Howitt and Sexton(1998).
Model Describtion
 WB Total renewable fresh water resources in the upstream
 country, Burkina Faso.
dW B   BW B dz B
 R-The runoff in downstream country, Ghana.
dR   Rdz
R
R
 αi i=B, G: The rate of water utilization of country i.
 wi i=B, G: The total per capita fresh water utilization in country i
wB =αB WB
 wG =αG WG =αG [(1- αB )WB+R]

Model Describtion(continued)
 S: The stock of water in the Akosombo Dam where hydropower is
 produced.
 dS=(1-αG})((1-αB)WB+R)dt,
 S(0) = S0
the state equation
SS
the minimum level (critical level) of water in
 the reservoir.
 Bi(wi): Benefit function for water consumption by country i.
 Ci(αi): Cost function for water irrigation by country i.
 Hi(S): Net consumer surplus from hydropower generation.
Burkina Problem
 Burkina Faso's maximization problem:



  r


B
B
J  E max
e NB d  
B 

t




dW   W dz
B
 subject to
 Net benefit of Burkina Faso
B
B
B
NB  B ( w )  C ( )
B
 And r -Discount rate (constant).
B
B
B
B
Ghana‘s problem
 Ghana's maximization problem:





 r
G
J G  E max
e
NB
d


G 
t


dS  (1 -  G )((1-  B )W B  R)dt
 subject to the state equation
 where W^B and R are given by the stochastic
equations
dW   W dz
 Net benefit of Ghana
B
B
B
dR   R Rdz R
B
NB  B (w )  H (S )  C ( )
G
G
G
G
G
G
Burkina Faso‘s water abstraction
 Burkina Faso will increase its water abstraction with
increase in variance in water supply irrespective of the
level of water realization.
 However, the rate of increase will be lower if the
country has concave marginal benefit function.
Ghana‘s water abstraction
 There exists an optimal value for the water abstraction
rate of Ghana, which will decrease or increase with the
increase in variances during low or high extreme
events respectively.
Ghana‘s reaction function
 Ghana will decrease its water abstraction with increase
in the water abstraction rates of Burkina Faso. The rate
of decline will be higher with increase in variance in
water supply caused by climate change.
Structure of the Game- A stochastic
Differential Stackelberg Game
 Burkina Faso moves first.
 Burkina Faso announces to the follower the policy rule
  (t )   S (t )
B
 Ghana taking this rule as given, seeks to maximize its
payoff, which yield the follower's reaction function.
 G (t )   ( S (t ), (.))
Burkina Faso knowing this reaction function,
chooses among all possible rules  (.) one that
maximizes its objective function.
Ghana‘s Problem
Assume quadratic policy rule for Burkina Faso
 B  aS 2  b



is known.


G
 r
G
J

E
max
e
NB
d

  

Ghana's maximization problem:

G
t
Subject to the state and flow equations, and constraint.

Burkina Faso‘s Problem
Assuming that the downstream country Ghana play the Markovian strategy,
 G ( S (t ), a (t ), b(t ))
the upstream country Burkina Faso chooses the optimal water abstraction
rate under cooperation by solving







J B  E max   e  r NB B d  
a ,b
t




subject to the same state and flow equations, and constraint.
Only difference is in the net benefit function
NB B  B B ( w B )  H B ( S ,  B )  C B ( B )
Ghana‘s Reaction Function Under
cooperation
Burkina Water abstraction with
cooperation
There exists an optimal value for the water abstraction
rate of Burkina Faso, which will
decrease with variance at higher level of water
abstraction
and increase with variance at lower level of water
abstraction respectively.
Ghana water abstraction
Water abstraction rate of Ghana will decrease in low
extreme event (drought)with the increase in variances.
However, the rate of decline will be lesser in the case
with higher level of cooperation.
Without co-operation
With co-operation
Burkina Faso will increase its water
abstraction with increase in variance
irrespective of low or high extreme
events
Burkina Faso will increase its water
abstraction with increase in variance
at lower level of water abstraction of
Burkina Faso while decrease its water
abstraction at higher level of water
abstraction of Burkina Faso
Ghana will decrease its water
abstraction with increase in variance
Ghana will decrease its water
abstraction with increase in variance
but the rate of decrease is much
lower here.
Ghana‘s water abstraction is at a
lower level
Ghana‘s water abstraction is at a
higher level
Ghana will decrease its water
abstraction if Burkina Faso increase
its water abstraction
If Burkina Faso increase its water
abstraction, Ghana will only decrease
its water abstraction during initial
phase of cooperation .
Comparison Chart
Conclusion
 How countries might gain from cooperation during climate
change?
 We have shown that issue linkage can help the countries
to cooperate in the event of climate change
 In a stochastic differential game, we have shown the
existence of equilibrium conditions for cooperation .
 Also the long run steady state is stable even with
increasing variances of water flow.
 Further applications-Central Asia
This paper could provide a theoretical basis in the
development of DSS-the model can provide outputs in a
time frame and based on past actions(markovian).
Thanks