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).
If it's worth saying, but not worth its own post, then it goes here.
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