The author is actually indireclty referring to the stable marriage problem ( http://en.wikipedia.org/wiki/Stable_marriage_problem , don't bother reading the paper the slate writer links to, it has no substantive content), in which you have two sets of agents which we label the "men" and the "women". Each agent has a preference ordering of the members of the other gender. It is really easy to prove that you can then find an equilibrium arrangement by iterating the following procedure i = 1..n:

have each man propose to the i'th woman on his list (if he's not currently matched, otherwise he does nothing). the woman accepts if she's not matched yet or if the man ranks higher on her list than the previous guy she accepted.

if you think for a moment you can see (and prove) that this equilibria favors the men.

Also curiously enough, this exact algorithm is used to match med students with residency programs