In this paper we investigate how the cooperation for an efficient international environmental

agreement can be encouraged. Until now all the types of the Environmental Treaties have been

based on multilateral agreements easily formalized using classic contract theory models that

emphasize the role of the compatibility with simple incentives for each countries. Assuming

the superadditivity in the coalition we know that once the coalition has formed the cooperation

within that coalition is unrestricted. Introducing the externality schemes and convexity we show

how the grand coalition is efficient.