international environmental agreements with uncertain environmental damage and learning michèle...
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International Environmental Agreements with Uncertain Environmental Damage and Learning
Michèle Breton, HEC MontréalLucia Sbragia, Durham University
Game Theory Practice 2011
IEA with uncertainty and learning
2
Outline
•Uncertainty and learning motivation•Literature•Model
▫Learning process▫Emission game
•Numerical approach & simulation•Results
▫Impact of uncertainty▫Impact of endogenous learning
IEA with uncertainty and learning
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Uncertainty & learning•e.g. impact of accumulated GHG on global
temperature (climate sensitivity)
• Is sometimes used to justify denied participation in IEAs : more information is required on the magnitude of damage before committing to costs
• Learning process: damage is observed as the stock of accumulated pollution increases
•Timing question: avoid irreversible damages vs unnecessary costs
“likely to be in the range 2 to 4.5◦C with a best estimate of about 3◦C, and is very unlikely to be less than 1.5◦C” (AR4)
IEA with uncertainty and learning
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This paper
•Impact of uncertainty and learning on emission decisions and welfare
•IEA in place with strategically interacting countries
•Simple environmental model with two key features▫dynamics of the pollution stock and of the
damage cost ▫negative externalities arising from
emissions
IEA with uncertainty and learning
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Literature
•Many papers on formation and stability of coalitions – in a certainty context
•Uncertainty & learning ▫ exogenous learning in two-stage games
(after/before the emission game, before the membership game) or static models
▫Single country with endogenous learning•Conclusion: uncertainty and learning are
both bad for cooperation and the environment
IEA with uncertainty and learning
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Our contributions•Consequences of uncertainty and
endogenous learning in terms of emissions and welfare▫Introduction of endogenous learning in a
dynamic emissions game▫Uncertainty can have either a positive or a
negative effect
•Sophisticated learning process vs simple mixed strategies▫Equilibrium welfare comparison
IEA with uncertainty and learning
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Model
•N players, of which s participate in an IEA•Revenues from production activity q •Emissions x from production activity•Damage from accumulated stock of
pollution P
jttt xPP 11
ttt dPPD )()( titit PDRW
itit xq itit
it qq
bR
2
ttt PdPD )()( ttt dPPD 2)(
IEA with uncertainty and learning
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The learning process•Countries do not know the real impact of
accumulated pollution – but observe the (noisy) damage
•Two possible states of the world (dH,dL)
•Bayesian updating of beliefs, where π represents the probability of high damage
)1,0(~, NPdD tttkt
)1)(|Pr()|Pr(|Pr(
1 πdDπdD )πdDπ LtHtHtt
IEA with uncertainty and learning
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The emission game
•Value function of a player satisfies
•Equilibrium strategies (strategic learning)
)),,(;),()1((
)1(2
max),(
PTxPOPVE PddxxbpPV LHx
)(*;)(*)1(()(*
)(*;)(*)1((),(*
ε,P,πTxsNsyδPVEγβbP,πγxε,P,πTxsNsyδPWEγβbπPγy
PπPπ
)),,(;),()1((
)1(2
max),(
PTsyPOPVE PddsyybspPW LHx
IEA with uncertainty and learning
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Special cases
•When uncertainty is resolved (steady-state)▫Linear damage function: constant
strategies
▫Quadratic damage function: strategies linear in P
•Mixed” strategy (myopic players)
kk
kk dbxsdby
LHLH xxx yyy
)1(
)1(
IEA with uncertainty and learning
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Numerical approach
•Finite difference approximation for the derivatives of the value function
•Fixed point (value iteration) algorithm for the value function
•Fixed point (cobweb) algorithm for the equilibrium strategies
•Interpolation of the value function by linear splines and analytic computation of expected values
IEA with uncertainty and learning
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Simulation10 true damage parameter 10
8
6,174
6,176
6,178
0 5 10 15
time
Pollution Stock
0
0.5
1
0 5 10 15
time
Belief
49.55
49.6
49.65
49.7
48.8
48.9
49
49.1
0 5 10 15
emissions
signatories Non-sig
0
20000
40000
60000
80000
100000
0 5 10 15
Damage
-
20,000
40,000
60,000
80,000
100,000
0 5 10 15
Welfare
IEA with uncertainty and learning
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Equilibrium results (linear case)•Equilibrium emissions of signatories and
non-signatories have similar behaviour with respect to belief and pollution stock▫Signatories always emit less than non-
signatories, more so when the damage parameter is believed high
▫Emissions are no longer constant in P : decreasing when is small and increasing when is large
IEA with uncertainty and learning
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Equilibrium emissions▫Can be higher than in the low damage, or
lower than in the high damage case
IEA with uncertainty and learning
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Equilibrium welfare▫Can be higher than in the low damage, or
lower than in the high damage case
IEA with uncertainty and learning
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Incentive to deviate▫Constant in P and generally increasing with
probability of high damage
IEA with uncertainty and learning
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Impact of uncertainty on emissions
•When the true damage parameter is low, players are more cautious and emissions are lower under uncertainty ▫Except when the probability of a high value for
the damage parameter is very low, in which case players emit more than in the certain case
•Conversely, when the true damage parameter is high, uncertainty has a negative impact as players generally emit more▫Except for very high values of the belief
IEA with uncertainty and learning
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Accounting for the dynamics of the learning process
IEA with uncertainty and learning
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Accounting for the dynamics of the learning process
IEA with uncertainty and learning
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Conclusions
•Impact of uncertainty and learning can be beneficial – or not▫Result is not the obvious one when belief is
“extreme”•Accounting for the dynamics of the
learning process can be beneficial or not – depending on the level of the belief in high environmental impact▫Higher welfare and higher emissions when
probability of high damage is less than 0.5
IEA with uncertainty and learning
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Conclusions
•Results are qualitatively similar with quadratic damage
•When learning is independent of the pollution level, equilibrium solution is very close to the myopic solution
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