Most people who have any interest in economics, game theory or even human psychology have heard of the Prisoner's Dilemma. PD is a big problem for free-market libertarists, because it undermines their claim that left to their own devices, people will always make rational choices and therefore state intervention is Evil. Problem is, when people do make rational decisions in cases involving the PD the result is far from optimal to most, if not all, concerned. There is also a thing called the Free rider problem which is closely related to PD. Things like social security and nature conservation are FRP's. People are unwilling to take part because they know it will take a lot of people to participite to make any difference. So there is the danger that their sacrifices are useless, thus it's better not to participate. And this is where the state is needed - to make everyone pay benefitting everyone in the long run.
I just read an article on the Traveller's Dilemma which is a variation of the Prisoner's Dilemma. What the studies mentioned in the article prove is that people are not rational beasts, required to make free-market society function better than one that is controlled to some degree by the state or other bodies. I don't believe in too much control either, but there needs to be something to control the worst outcomes that free-market libertarism could come up with.
Funny thing is, these dilemma's are more or less intuitive in nature, yet many refute them. This, in my opinion, proves that for some economics isn't a science but a religion. If reality clashes with theory, reality is wrong. This is actually one of the main separating factors between science and religion. The former is preparead to change it's theories, latter is not. Of course the other major difference is is that science requires that results must be repeatable.
That's why it's usually so hard to have a rational discussion with libertarians. It's just like trying to argue a believer that his belief system is wrong which is completely impossible. Well, ok, you can try to argue but it will never lead anywhere.