A two-level differential game of international emissions trading

In this paper we propose a dynamic game theoretic modeling framework for the international climate change negotiations that should take place, at the end of the Kyoto protocol agreement, if the necessity to curb drastically carbon emissions is confirmed. The model is composed of a set of optimal economic growth models corresponding to the different groups of nations that will be parties in the negotiations. Emissions of greenhouse gases are represented as by-products of the economic production process. Two types of capital (clean vs. dirty) can be used to produce the economic good with different emissions effects. The negotiations should determine a set of allowances that define caps on GHG emissions such that a long term constraint on total emissions is satisfied. At each instant of time, given the emission caps, an international emissions trading system is organized. In order to be self-enforcing the emission caps, and the economic growth paths have to satisfy a noncooperative equilibrium condition. We describe mathematically this two-level game structure and give the necessary optimality conditions that have to be satisfied by the equilibrium solution, under the coupled global emission constraint.