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

TL;DR

The paper tackles a sequential, two-sided platform optimization problem where both users and creators can exit if engagement falls short, formalizing a model where long-run engagement is maximized under participation constraints. It shows that a naive, user-centric approach can be arbitrarily bad and that the general two-sided problem is NP-hard to approximate; the Forward-Looking framework links optimal long-run performance to maximum stable sets, enabling an ILP formulation. To bridge theory and practice, the authors introduce two polynomial-time algorithms, Local Clustering and Creator Ranking with Potential Audience Size, that offer constant-factor guarantees under mild density assumptions and robust empirical performance via augmenting-path techniques. The work advances understanding of platform design under two-sided dynamics and provides practical tools for sustaining engagement in real-world two-sided markets. It highlights the importance of accounting for both sides’ incentives and departures in recommendation systems, with potential implications for social networks, streaming platforms, and marketplace ecosystems.

Abstract

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.

Figures (15)

• Figure 1: Illustration of Example \ref{['example:model_simple']}
• Figure 2: Outline of the proof sketch of Proposition \ref{['prop:submodular_fixU']}. Vertices in this figure indicate matchings between the specified sets of users and creators that satisfy all constraints. Edges in this figure indicate relocation graphs that capture changes from one matching to another: for example, $G^1$ represents changes from $R$ to $R^1$. The left hand side of \ref{['eqn:submodular_fixU']} is the sum of edge weights of $G^{0,1}$ (red edge), and the right hand side is lower bounded by that of $G^0$ (violet edge).
• Figure 3: Reduction of a possible input graph to a user-creator instance in Theorem \ref{['thm:hard']}, and a stable set that corresponds to an independent set
• Figure 4: Illustration of Example \ref{['example:model_megacrown']}
• Figure 5: Illustration of Example \ref{['example:model_cascade']}

Theorems & Definitions (64)

• Example 1
• Remark
• Definition 1: Forward-Looking
• Definition 2: Stable set
• Proposition 1
• Theorem 1: Approximability without user constraints
• Proposition 2: Submodularity when users are fixed
• Theorem 2: Inapproximability of the general model
• Definition 3: User-Centric
• Theorem 3