This paper deals with the modeling of the strategic allocation of greenhouse gases emission allowances in the EU-wide trading market that results from Kyoto agreement implementation. An M-matrix game is formulated where the players are countries or groups of countries that may have a strategic influence through their allocation of emission allowances and the payoffs are the welfare gains of these countries, evaluated from a multi-country computable general equilibrium model. To solve the matrix game one uses the concept of correlated equilibrium which makes sense in the context of EU negotiations. One studies several formulations of that two-level game structure and, in all these instances, we obtain a unique equilibrium solution that can be given an interesting interpretation for establishing a scheme for greenhouse gas emission allowance trading within the community.