  Many online platforms of today, including social media sites, are two-sided
markets bridging content creators and users. Most of the existing literature on
platform recommendation algorithms largely focuses on user preferences and
decisions, and does not simultaneously address creator incentives. We propose a
model of content recommendation that explicitly focuses on the dynamics of
user-content matching, with the novel property that both users and creators may
leave the platform permanently if they do not experience sufficient engagement.
In our model, each player decides to participate at each time step based on
utilities derived from the current match: users based on alignment of the
recommended content with their preferences, and creators based on their
audience size. We show that a user-centric greedy algorithm that does not
consider creator departures can result in arbitrarily poor total engagement,
relative to an algorithm that maximizes total engagement while accounting for
two-sided departures. Moreover, in stark contrast to the case where only users
or only creators leave the platform, we prove that with two-sided departures,
approximating maximum total engagement within any constant factor is NP-hard.
We present two practical algorithms, one with performance guarantees under mild
assumptions on user preferences, and another that tends to outperform
algorithms that ignore two-sided departures in practice.
