  We study the stable marriage problem in two-sided markets with randomly
generated preferences. We consider agents on each side divided into a constant
number of "soft tiers", which intuitively indicate the quality of the agent.
Specifically, every agent within a tier has the same public score, and agents
on each side have preferences independently generated proportionally to the
public scores of the other side.
  We compute the expected average rank which agents in each tier have for their
partners in the men-optimal stable matching, and prove concentration results
for the average rank in asymptotically large markets. Furthermore, we show that
despite having a significant effect on ranks, public scores do not strongly
influence the probability of an agent matching to a given tier of the other
side. This generalizes results of [Pittel 1989] which correspond to uniform
preferences. The results quantitatively demonstrate the effect of competition
due to the heterogeneous attractiveness of agents in the market, and we give
the first explicit calculations of rank beyond uniform markets.
