Controlling the international stock pollutant with policies depending on target values

In this paper a stochastic dynamic game formulation of the economics of international environmental agreements on the transnational pollution control, when the environmental damage arises from stock pollutant that accumulates, for accumulating pollutants such as CO2 in the atmosphere is provided. To improve the non-cooperative equilibrium among countries, we propose a different criterion to the minimization of the expected discounted total cost. Moreover, we consider Cooperative versus Noncooperative Stochastic Dynamic Games formulated as Markov Decision Processes (MDP). We propose a new alternative where the decision-maker wants to maximize the probability that some total performance of the dynamical game does not exceed a target value during a fixed period of time. The task requirements are therefore formulated as probabilities rather than expectations. This approach is different from the standard MDP, which uses performance criteria based on the expected value of some index. We present properties of the optimal policies obtained under this new perspective.