A time-consistent model for cooperation in international pollution control

In this paper, transnational pollution is formulated as a differential game between sovereign governments. We consider the case when the countries want to cooperate and agree to act so that an international optimum can be achieved. For the cooperative scheme to be upheld throughout the game horizon, both group rationality and individual rationality are required to be satisfied at any point in time along the optimal trajectory. A payment distribution scheme is formulated to guarantee time consistency. We conclude that a payoff transfer is not necessary to ensure cooperation given that the countries are different only in environmental efficiency. However, if the countries differ in terms of damage parameters, a payoff transfer from the country with higher damage parameters to the country with lower damage parameters is required for the time-consistent cooperative solution.