Matching of Users and Creators in Two-Sided Markets with Departures

Many online platforms of today, including social media sites, are two-sidedmarkets bridging content creators and users. Most of the existing literature onplatform recommendation algorithms largely focuses on user preferences anddecisions, and does not simultaneously address creator incentives. We propose amodel of content recommendation that explicitly focuses on the dynamics ofuser-content matching, with the novel property that both users and creators mayleave the platform permanently if they do not experience sufficient engagement.In our model, each player decides to participate at each time step based onutilities derived from the current match: users based on alignment of therecommended content with their preferences, and creators based on theiraudience size. We show that a user-centric greedy algorithm that does notconsider creator departures can result in arbitrarily poor total engagement,relative to an algorithm that maximizes total engagement while accounting fortwo-sided departures. Moreover, in stark contrast to the case where only usersor 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 mildassumptions on user preferences, and another that tends to outperformalgorithms that ignore two-sided departures in practice.