  Thick two-sided matching platforms, such as the room-rental market, face the
challenge of showing relevant objects to users to reduce search costs. Many
platforms use ranking algorithms to determine the order in which alternatives
are shown to users. Ranking algorithms may depend on simple criteria, such as
how long a listing has been on the platform, or incorporate more sophisticated
aspects, such as personalized inferences about users' preferences. Using rich
data on a room rental platform, we show how ranking algorithms can be a source
of unnecessary congestion, especially when the ranking is invariant across
users. Invariant rankings induce users to view, click, and request the same
rooms in the platform we study, greatly limiting the number of matches it
creates. We estimate preferences and simulate counterfactuals under different
ranking algorithms varying the degree of user personalization and variation
across users. In our case, increased personalization raises both user match
utility and congestion, which leads to a trade-off. We find that the current
outcome is inefficient as it lies below the possibility frontier, and propose
alternatives that improve upon it.
