Jeremy Rifkin dealt with this issue extensively in his book The Zero Marginal Cost Society in which he predicted the rise of the "Collaborative Commons" as a successor to capitalism. I previously discussed the book and explained how innovations like Steem can facilitate the advent of the predicted Commons: https://steemit.com/steem/@sean-king/why-steem-means-the-decline-of-capitalism-and-the-rise-of-the-collaborative-commons
In the book he goes to great lengths to destroy the whole idea of the Tragedy of the Commons. He demonstrates that the Tragedy is rarely observed in reality and that most advocates of the Tragedy idea president a false choice between allocating resources via either markets or central planning or suffering unregulated pillage of those resources (the co-called Tragedy of the Commons).
This choice is false because in reality people develop other ways of regulating use of resources besides governments and markets. He provides example after example--some quite ordinary and some pretty fantastic--of how human culture regulates such things through custom, shaming/ostracism, technology, etc.
I can't really do the topic justice in a comment, so I'd encourage anyone with an interest in the subject to read his book or my summary at the link above.
RE: Should anarchists abolish the commons?