Yes. It's called a coordination problem: http://raikoth.net/libertarian.html#coordination_problems
But for example, why would other people let Mike pollute the water despite everyone else having signed the "Filter Pact"? Mike's selfish actions would directly affect other people making a living, and therefore, some kind of intervention would be warranted - and would happen too! After that, everything is fine again.
Even if you're silly enough to argue against your own freedom, you can't just leave things at presenting a problem, expecting it would not get solved, and thinking you've proven that freedom "doesn't work".