GPs example is exactly game-theoretix tragedy of the commons / prisoners dilemma.
> Tragedy of the Commons is what happens when nobody clearly owns something that many people use, so none of them use it responsibly.
It's specifically, originally, a term for overgrazing a pastureland resulting from the kind of arrangement you described; there are a number of generalizations from that example which have been given the name, including both the one you describe, and the even more general condition in which each player has a dominant strategy of defection even though all players cooperating has a better payoff than all defecting.
The Commons need not be an overgrazed pastureland; it can be any open access resource. The best modern example would be Earth's atmosphere and how its being filled with pollution. GGP has not specified a Commons and the existence of one is not implied in his comment.
The fact that the term has long been widely accepted as a label for the general class of problems, OTOH, does.
(Arguably, the structure of the payoff matrix in the class of problems implies an economically real if intangible “commons” in any problem in the class, which is probably why the label is used that way.)
The overall effect is more uncertain than you suggest, but presumably it's clear that the 'giving' that is highly desired and publicly demanded by certain people can be implemented by them today.
Further, I'd postulate that the desire to only give if everyone gives is a rather convenient mechanism to simultaneously not give and appear virtuous.
Tragedy of the commons is not a new concept.