It's not a prisoner's dilemma.

A prisoner's dilemma is a wholly fictional and game-theoretic construct involving single, isolated interactions among perfectly rational agents.

None of that has anything to do with humans. Humans never play the prisoner's dilemma because they're never any of the above concepts. Humans are certainly not perfectly rational, and almost always interact with the same set of people. You can't apply such an abstraction to public policy.