1. International Environmental Agreements with Uncertain Environmental Damage and Learning Michèle Breton, HEC Montréal Lucia Sbragia, Durham University Game Theory Practice 2011

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 2

3. 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 IEA with uncertainty and learning 3 “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)

4. 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 4

5. 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 5

6. 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 6

7. 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 IEA with uncertainty and learning 7

8. The learning process Countries do not know the real impact of accumulated pollution – but observe the (noisy) damage Two possible states of the world (d H,d L ) Bayesian updating of beliefs, where π represents the probability of high damage IEA with uncertainty and learning 8

9. The emission game Value function of a player satisfies Equilibrium strategies (strategic learning) IEA with uncertainty and learning 9

10. Special cases When uncertainty is resolved (steady-state) ▫Linear damage function: constant strategies ▫Quadratic damage function: strategies linear in P Mixed” strategy (myopic players) IEA with uncertainty and learning 10

11. 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 11

12. Simulation IEA with uncertainty and learning 12

13. 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 13

14. Equilibrium emissions ▫Can be higher than in the low damage, or lower than in the high damage case IEA with uncertainty and learning 14

15. Equilibrium welfare ▫Can be higher than in the low damage, or lower than in the high damage case IEA with uncertainty and learning 15

16. Incentive to deviate IEA with uncertainty and learning 16 ▫Constant in P and generally increasing with probability of high damage

17. 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 17

18. Accounting for the dynamics of the learning process IEA with uncertainty and learning 18

19. Accounting for the dynamics of the learning process IEA with uncertainty and learning 19

20. 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 20

21. 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 IEA with uncertainty and learning 21