Unfortunately, using game theory to model complex human interactions is severely flawed: it falls into its own Gödelian trap, where those setting the "rules" are, presumably, acting in their own self-interest within the system, the very same accusation made of civil servants and others who believed themselves to be acting for the public good. The ultra-libertarian view of "giving people what they want" seems conveniently to ignore the fact that human nature makes people tend to want something for nothing, if they believe they can get it. We all believe other people should be the ones paying more taxes.
Archive footage in the programme showed Berlin himself making a convincing argument against positive freedom: that, as it was the ultimate solution, any price was worth paying for it, and therefore any system intended to provide positive freedom would inevitably lead to tyranny and terror, the Soviet Union being a recent obvious example. Yet the "negative freedom" deployed by the neo-Conservatives in the USA is sinister and hardly reassuring, either. The programme concluded by saying that Berlin was wrong, but it had no alternative to put forward. Berlin also denounced paternalism in the programme, but that seems to me to be mistaken. Of course the danger is that paternalism is patronising and condescending, and it has its own Gödelian self-reference problem, but it is also appealing to human nature to have someone else to take all of the difficult decisions away from us, reassuring us that it will all be all right in the end.