Abstract
The purpose of this paper is to investigate a stochastic differential game of transboundary pollution and environmental policy.
We considered two asymmetric countries. The production process results in the emission of pollutants that are added to the existing stock common to both countries. The pollution accumulation dynamics is affected by an additive shock, the mean and variance are known. In both countries, the government controls emission levels. Uncertainty is incorporated into the model through a shock. The stock of pollution evolves stochastically according to geometric Brownian motion. In order to maximize the expected net present value of social welfare, the two governments should set the emission levels.
We formulate stochastic differential games that need to be solved by the two governments and derive unique Markov-perfect Nash and cooperative equilibrium solutions. Subsequently, we propose a mechanism to derive the payoff distribution procedures of subgame consistent solutions in cooperative stochastic differential games for the two governments, and are able to derive a subgame consistent solution based on the Nash bargaining axioms.
In conclusion, we show how the governments agree to maximize the sum of their expected payoffs and divide the total cooperative payoff so that the Nash bargaining outcome is maintained at every instant of time. Moreover, we show conditions guaranteeing individual rationality.
JFL Classification: F18, L13, Q58
