This paper aims to provide a comprehensive explanation for the likely failure in the decoupling of economic growth from environmental degradation, and also intends to offer perspectives on the new role of competition in a steady state or a degrowth economy. The analysis is based on five different scenarios, and uses the European Union as an example. It is concluded that we must prepare ourselves for a potential incompatibility between sustainability and economic growth. In this respect one can say that the current EU situation is in some ways already quite close to an economic system without growth, although far from sustainable as yet. Two of the four perspectives developed, regarding the new role of competition in an economy without growth, indicate an increase of direct and indirect competition over resources. The other two perspectives point out that regulatory public intervention as well as financial intervention will increase in order to ensure that - despite the revised role of competition - the poorest are still given a chance to develop (e.g. through basic minimum incomes), even in a degrowth economy.