Cooperation in a Dynamic Setting with Asymmetric Environmental Valuation and Responsibility

We analyze an environmental agreement as a cooperative differential game between two regions. The agreement is jointly profitable, since the current contributions in terms of emissions reduction is overcompensated by the benefits of a cleaner environment now and in the future. The regions are asymmetric in two respects: the valuation of a cleaner environment and the responsibility for the state of the environment at the beginning of the agreement. Unlike standard dynamic distribution schemes, the proposed mechanism distributes the efforts of lowering current emissions, not the benefits of a cleaner environment. It is built following an axiomatic approach. It must be time consistent: At any intermediate time, no country can do better by deviating from cooperation. A benefits pay principle is also required: The greater one region’s relative benefit from cooperation, the greater must be its relative contribution. A novelty of our approach is the addition of a responsibility or polluter pay principle: A region’s relative contribution increases with its responsibility. We characterize a family of dynamic distribution schemes which satisfy the three desired axioms. Interestingly, the proposed scheme could equivalently arise from the Nash bargaining solution considering an asymmetric bargaining power.