The Importance of Knowing the Distribution of Mistakes

There's a phrase that I think it was Bernard, false from Bernard Williams used by Utiliterianism. They called government house utilitarianism and what he meant was like the idea that a utilitarian who wants people to be content because they think that overall, you'll get the best results if people believe the false theory. So then government house utilitarian is not part of game theory, according to that definition. That's puzzling to me. It could still be true that knowing game theory isn't changing your behavior once you know game theory. And that adds an interesting complexity to social and human sciences.