The core of an economy with a common pool resource: A partition function form approach

In this paper we consider a model of an economy with a common pool resource. Under decreasing returns to scale, it is well-known that no Nash equilibrium attains Pareto efficiency. We examine whether it is possible to achieve Pareto efficiency and avoid the tragedy of the commons through cooperation among players. For that purpose, we use the notion of a game in partition function form. Whether or not the core exists depends crucially on the expectations of each coalition regarding the coalition formation of the outsiders. If each coalition has pessimistic expectations, then the core always exists, while if it has optimistic expectations, the core may be empty.