I suspect that there is some mathematical formalism which describes how the tragedy of the commons turns into an iterated PD, where virtues such as fairness and honesty emerge naturally, but I cannot find anything relevant online.
Well, I was just sort of making stuff up, so I'm not surprised there no literature :P
But what was going through my head was that a one-shot game can be turned into an iterated game just by breaking the decisions and payoff into pieces and setting it up so that people share information at regular intervals unless they pay a prohibitive cost. Depending on the real-world situation, this may just be a different framing of the same thing - e.g. the rats on a Malthusian island.
Many players vs. two players seems like the bigger gulf between tragedy of the commons...
This is prompted by Scott's excellent article, Meditations on Moloch.
I might caricature (grossly unfairly) his post like this: