Most problems faced by modern human society have two characteristics in common--they are tragedy-of-the-commons type of problems, and they are global problems. Tragedy-of-the-commons type of problems are those where a commonly shared resource is overexploited by free riders at the expense of everyone sharing the resource. The exploitation of global resources such as clean air and water, political stability and peace, etc. underlies many of the most pressing human problems. Punishment of free riding behavior is one of the most frequently used strategies to combat the problem, but the spatial reach of sanctioning institutions is often more limited than the spatial effects of overexploitation. Here, we analyze a general game theoretical model to assess under what circumstances sanctioning institutions with limited reach can maintain the larger commons. We find that the effect of the spatial reach has a strong effect on whether and how the commons can be maintained, and that the transitions between those outcomes are characterized by phase transitions. The latter indicates that a small change in the reach of sanctioning systems can profoundly change the way the global commons can be managed.