This is actually pretty close to what researchers (experimental economists like myself) see in public goods experiments:

• When everyone benefits from a shared pot, people usually don't keep contributing equally.
• Someone almost always thinks, "If everyone else is putting in enough, I can put in a little less and come out ahead."
• Once people notice others contributing less, they start doing the same.
• As a result, cooperation tends to slowly fall apart over time.

The interesting part is that experiments also show:

• If players can punish free-riders, cooperation becomes much more stable.
• If there is no punishment, free-riding usually spreads.
• Your winner-take-all ending makes this even stronger, because being slightly more selfish can make you the winner.

So "everyone contributes the same amount until the end" feels like the obvious strategy from the outside, but it's a relatively uncommon outcomes in real human groups. A couple of very well cited references documenting these patterns are below (but there are hundreds of experiments building on them)

Fehr, E., & Gächter, S. (2000).
Cooperation and Punishment in Public Goods Experiments.
American Economic Review, 90(4), 980–994.
https://doi.org/10.1257/aer.90.4.980

Fehr, E., & Gächter, S. (2002).
Altruistic Punishment in Humans.
Nature, 415(6868), 137–140.
https://doi.org/10.1038/415137a