This is a humorous graph theory problem, and I would love some pointers here. I'm finding the concept of matching a little challenging, so I'm not sure where to start.
Suppose we have $n$ pairs of girlfriends (with a total of $2n$ girls), another set of $2n$ boys. We want to romantically match each girl to a guy such that the girl can beat the guy at poker. Given any pair of girlfriends, say the $i$th pair, both girls in the pair can defeat at least $2i -1$ boys at poker. Also, if a girl cannot defeat a guy at poker, then her other girlfriend in the pair can defeat him. Can we find a matching so that each girl defeats her guy?