Time consistent side payments in a dynamic game of downstream pollution

This note determines a rule to share a surplus gained when two countries or regions agree to coordinate their policies to reduce downstream pollution. An intertemporal decomposition scheme for the total side payment is proposed. This scheme has the following individual rationality property: in each subgame that starts along the cooperative trajectory, one country is guaranteed to receive a higher payoff in the cooperative solution than in the disagreement solution. For this country another notion of individual rationality obtains: this country will at any instant of time during the play of the game receive a higher payoff in the cooperative solution than in the disagreement solution.