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

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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

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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

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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

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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

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Equilibrium welfare▫Can be higher than in the low damage, or

lower than in the high damage case

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Incentive to deviate▫Constant in P and generally increasing with

probability of high damage

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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

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Accounting for the dynamics of the learning process

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Accounting for the dynamics of the learning process

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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

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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