Some cool 'challenge' maths questions I came up with:
$i) In a 2 player game where $|A_1| = n$, $|A_2| = m$, and all payoff values are distinct, show that there can be no more than $\min(n,m)$ Nash equilibria.
$ii) You are now given that $n = m$, and furthermore that there are precisely $n$...