Controlling the International Stock Pollutant in Markov Decision Processes with Policies Depending on Target Values∗

In this paper we provide a stochastic formulation of the economics of international agreements on transnational pollution control, when the environmental damage arises from stock pollutant that accumu-lates. To improve the non-cooperative equilibrium among countries we propose a different criteria to the minimization of the expected discounted total cost, with possibly monetary transfers as incentive. We consider Stochastic Dynamic Games formulated as Markov Decision Processes (MDP) and Cooperative versus Non-cooperative (dynamic) Games. Moreover we propose a new alternative, where the decision-maker wants to maximize the probability that some total per-formance 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 use performance criteria based on the expected value of some index. We present properties of the optimal policies obtained under this new perspective