  Motivated by online dating apps, we study how to select subset of profiles to
show to each user in each period in a two-sided matching platform. Users on
each side observe the profiles set by the platform and decide which of them to
like. A match occurs if and only if two users mutually like each other,
potentially in different periods. The goal of the platform is to maximize the
total expected number of matches. We study different platform designs, varying
(i) how users interact with each other, i.e., whether one or both sides of the
market can initiate an interaction, and (ii) the timing of matches, i.e.,
whether the platform allows non-sequential matches in addition to sequential
ones. We focus on the case with two periods and study the performance of
different approaches. First, we show that algorithms that exploit the
submodularity of the problem and properties of its feasible region can achieve
constant factor approximation guarantees that depend on the platform design,
ranging from $1-1/e$ to $1/3$. Finally, we show that the Dating Heuristic (DH)
(Rios et al., 2023), which is commonly used and achieves good performance in
practice, provides an approximation guarantee of $1-1/e$ for all platform
designs. We show theoretically and empirically that the performance of the DH
is robust to the platform design. Our simulation results -- using real data
from our industry partner -- also show that platforms using a one-directional
design should initiate interactions with the side that leads to the smallest
expected backlog per profile displayed, balancing size and selectivity.
Moreover, we find that a one-directional design can lead to at least half of
the matches obtained with a two-directional design. Finally, our results show
that avoiding non-sequential matches has no sizable effect, regardless of the
platform design.
