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blacktrance comments on What rationality material should I teach in my game theory course - Less Wrong
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Make sure to emphasize that payoffs are in terms of utility, and that when money is used as a payoff, it's meant to be a substitute for utility. This will hopefully prevent people from saying things like "According to game theory, all people care about is money! So game theory is wrong". If your students don't know what utility is, that should be the first thing you teach them, and it may help to give a few reminders over the course of the class.
This is important, but unfortunately for me many of the students will have spent a huge amount of time studying utility whereas many others will have never heard of it so I just end up saying if you know what utility is than the payoffs are utility if not than all you care about in life is getting the highest payoff and the payoff might include stuff other than money.