In this paper a linear-quadratic emissions game is used to analyze the stability of international environmental agreements (IEA) taking explicitly into account the non-negative constraint on emissions. Our results show that the higher the environmental damages are the higher the number of countries in a self-enforcing is always that the countries in the agreement enjoy a leadership position. Without this strategic advantage, i.e. under Cournot conjecture, we show that the maximum level of cooperation consists of two countries, independently of the number of countries in the game and the scope of the gains to full-cooperation.