The core allocations in the economy with environmental externalities are necessary for forming voluntary environmental coalitions. Identifying the scope or ‘size’ of the core allocations are of vital importance to policy guidance in supporting such coalition. In this paper, a cooperative game of stock externality provision is constructed; the criteria for assessing core allocations are developed; the methods and algorithms of calculating the ‘size’ of the core are derived. The game is implemented and solved in the RICE model (Nordhaus and Yang, 1996). The ‘sizes’ of the cores in the RICE models with different number of regions are calculated. The results show that the size of the core shrinks as the number of regions increases. Finally, the policy implications of shrinking core phenomenon are indicated.