  In this work, we analyze the influence of a single strategic agent on the
quality of the other agents' matchings in a matching market. We consider a
stable matching problem with $n$ men and $n$ women when preferences are drawn
uniformly from the possible $(n!)^{2n}$ full ranking options. We focus on the
effect of a single woman who reports a modified preferences list in a way that
is optimal from her perspective. We show that in this case, the quality of the
matching dramatically improves from the other women's perspective. When running
the Gale--Shapley men-proposing algorithm, the expected women-rank is $O(\log^4
n)$ and almost surely the average women-rank is $O(\log^{2+\epsilon}n)$, rather
than a rank of $O(\frac{n}{\log n})$ in both cases under a truthful regime. On
the other hand, almost surely, the average men's rank is no better than
$\Omega\left(\frac{n}{\log^{2+\epsilon}n}\right)$, compared to a rank of
$O({\log n})$ under a truthful regime. All of the results hold for any matching
algorithm that guarantees a stable matching, which suggests that the core
convergence observed in real markets may be caused by the strategic behavior of
the participants.
