I'm actually very familiar with the idea of the tragedy of the commons.

Rather than re-cover well tread ground, I hope that you don't mind if I quote from a relevant section of an Anarchist FAQ, and I encourage you to check the link I shared, as it goes into far more detail:

In reality, the "tragedy of the commons" comes about only after wealth and private property, backed by the state, starts to eat into and destroy communal life. This is well indicated by the fact that commons existed for thousands of years and only disappeared after the rise of capitalism -- and the powerful central state it requires -- had eroded communal values and traditions. Without the influence of wealth concentrations and the state, people get together and come to agreements over how to use communal resources and have been doing so for millennia. That was how the commons were successfully managed before the wealthy sought to increase their holdings and deny the poor access to land in order to make them fully dependent on the power and whims of the owning class.

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In fact, communal ownership produces a strong incentive to protect such resources for people are aware that their offspring will need them and so be inclined to look after them. By having more resources available, they would be able to resist the pressures of short-termism and so resist maximising current production without regard for the future. Capitalist owners have the opposite incentive... unless they maximise short-term profits then they will not be around in the long-term (so if wood means more profits than centuries-old forests then the trees will be chopped down). By combining common ownership with decentralised and federated communal self-management, anarchism will be more than able to manage resources effectively, avoiding the pitfalls of both privatisation and nationalisation.

If you want a modern, real-world example of this which you may have actually experienced yourself, look no further than this medium we are using to communicate. The Internet is a great example. The Internet was a fantastic common space lovingly maintained and curated by individuals, with services and content provided freely. Corporations encircled it, and turned it into the torment nexus we have today. It wasn't because of us, collectively, that spoiled the commons of the Internet - it was capitalism itself.