A multistage supergame of downstream pollution

We consider two neighbouring regions whose pollution emissions damage their common environment. Mathematically the problem is formulated as a mull-stage supergame. At each stage, the players decide to cooperate or not during the time interval separating two successive stages. On this time interval, a non zero-suns game is defined. Under a cooperative regime, the players agree to apply the Nash bargaining solution. If a non cooperative regime prevails, the players get the Nash equilibrium outcomes. The structure of the optimal behaviour in the supergame is fully characterised, and time consistency of the solution investigated.