I’m not sure about the level of rigor you’re looking for; whether this is supposed to be a fun, short assignment, or something less accessible. This doesn’t really go into any mathematics, but shows the interesting and even entertaining side of game theory pretty well:
There’re also Douglas Hofstadter’s writings on game theory, which, like pretty much everything of his, are a joy to read (for me, at least). I wouldn’t quite say he uses game theory to “explain something,” but whatever he does do achieves a similar goal. Unfortunately, the only PDF I could find (not that I looked very hard) is very poorly formatted; I recommend searching it for “Dilemmas for Superrational Thinkers” or going for the Post Scriptum starting on page 31, as those are both particularly interesting parts (in different ways).
I hope one of these was helpful.
It can be worthwile to figure out specifically how something that goes wrong, actually does go wrong. In the interest of helping with that, I’ll try to add something to all the other criticisms that people have already made here.
The author actually makes a lot of mostly plausible arguments; they’re not all accurate or useful (in particular, a lot seem to be in the form of “here’s a reason why AI might not be a risk, with no thought going into how likely it is,” which is only marginally helpful), but they’re understandable, at least. What’s especially concerning, though, is that they also invoke the absurdity heuristic, and actually seem to think it’s the most important part of their argument. They spend more time on “this idea is silly and is connected to other ideas that are silly” than any one of those other “plausible” arguments, which is really bad practice. To some extent this is understandable, because it was a talk and therefore supposed to be somewhat entertaining, and pointing and laughing at weird ideas is certainly entertaining, but they went too far, I think.