On the core of an economy with multilateral and multidimensional environment externalities

For simple economic models of transfrontier pollution, Chander and Tulkens (1995) and (1997) have offered a formula for transfers to sustain international cooperation on a voluntary basis and which deter coalitionnal free-riding under some reasonable behaviours of countries not in the coalition. Their scheme rests on the assumption that pollution is a scalar. Relaxing this assumption, interesting interactions among pollutants arise that call for a new formula. In this paper we extend Chander and Tulkens formula for this more realistic multidimensional context, and thereby enhance the pratical and theoretical relevance of their seminal analysis.