Abstract
The purpose of this study was to investigate international cooperation on pollution control between asymmetric countries under uncertainty. We considered any two countries that are asymmetric with respect to their technological level and the amount of environmental damage they incur. Production processes result in the emission of pollutants that are added to the existing pollution stock common to both countries. The stock of pollution evolves stochastically, according to the geometric Brownian motion. The governments of the two countries set their pollutant emission levels at the Markov perfect equilibrium to maximize their expected net present value of social welfare. In addition, they set their pollutant emission levels at cooperative equilibrium to maximize the sum of their expected net present value of social welfare.
In cooperative stochastic differential games, a credible cooperative agreement must be subgame consistent. Subgame consistency ensures extension of an optimal policy to a later starting time, and any possible state brought about by prior optimal behaviour of the governments remains optimal.
We considered a cooperative game in which the governments of two countries agree to maximize and divide the sum of their expected net present value of social welfare in a way that shares the gain from their cooperation proportional to the relative sizes of their expected non-cooperative net present value of social welfare at every instant of time. In conclusion, the country with a higher technological level or that incurs lower environmental damage obtains a larger instantaneous payoff at the subgame consistent solution.
JEL Classification: F18, L13, Q58
