Subgame Consistent Solution for a Cooperative Differential Game of Climate Change Control

After several decades of rapid technological advancement and economic growth, alarming levels of pollutions and environmental degradation are emerging all over the world. Moreover, it is now apparent that human activities are perturbing the climate system at the global scale leading to disturbances to complex ecological processes. In this paper, we present a cooperative differential game of climate change control. Climate change is incorporated as structural changes in the pollution dynamics and the payoff functions. The policy instruments of the game include taxes, abatement efforts and production technologies choices. Under cooperation, nations will make use of these instruments to maximize their joint payoff and distribute the payoff according to an agreed upon optimality principle. To ensure that the cooperative solution is dynamically consistent, this optimality principle has to be maintained throughout the period of cooperation. An analytically tractable payment distribution mechanism leading to the realization of the agreed upon imputation is formulated. This analysis widens the application of cooperative differential game theory to environmental problems with climate change. This is also the first time differential games with random changes in the structure of their state dynamics.