That kind of comparison doesn't work because you can't get a tragedy of the commons situation in minecraft. All you really need is wood and stone, trees regrow extremely quickly, and stone is effectively infinite.

"Within a week, trees were in short supply."

If you're implying minecraft in general, then yes. Otherwise in this particular case, resources seemed to be all finite.

The following things are "infinite" if you forbid exploration into new areas:

* Water

* Lava Flows (Sources are finite)

* Wood/charcoal: if you have enough saplings and dirt.

* Cobblestone: if you have lava and water in the correct arraignment

* Wheat: if you have enough seeds and dirt

* Fish: if you have water

* Neutral-Monster items: for those monsters you can breed if you maintain the habitat

* Aggro-monster items

I believe that's it

There are a few random others. Apples should be infinite, since they come from trees. Other plant-ish things as well, like melon or pumpkin, provided you have any in the first place.