I asked him to give me an intuitive explanation of Nash's theorem, and, while the details are lost to memory, I remember having one of those thrilling epiphanies as he explained how it followed from Brouwer's fixed point theorem.
There was supposed to be required coursework, but every week I'd come into his office and ask questions like that, and we'd end up talking the whole time, often long after the hour was over. Grades and homework didn't seem to matter much to him. It's incredible to think now how much excitement and passion he mustered for the curiosity of a novice.
RIP, Prof Shapely.
I remember the Shapley-Shubik power index [1], used to measure someone's voting power. Roughly, you imagine the voters vote one at a time, imagine all possible orders in which they could vote, and count the percentage of permutations in which your vote is the one that makes the step from "less than majority" to "majority". (The subject of the vote is a binary choice.)
I remember thinking the Banzhaf power index [2] was better. I learned about all this from a CTY summer class called "Game Theory and Strategy". I didn't know how to program back then, and I might profit from rethinking the concepts...
[1] https://en.wikipedia.org/wiki/Shapley%E2%80%93Shubik_power_i...
https://en.wikipedia.org/wiki/Stable_marriage_problem
And an application that builds on his work;
https://en.wikipedia.org/wiki/National_Resident_Matching_Pro...