Algorithmic Content Selection and the Impact of User Disengagement

TL;DR

The paper addresses how algorithmic content selection should balance immediate revenue with long-term user engagement in the presence of friction and evolving user satisfaction. It develops a stateful model where engagement probability depends on a cumulative satisfaction measure, introducing a dynamic discounting reformulation via a modified discount factor $ ilde f(x)$. The authors derive efficient offline and online solutions, including a DP for $k$-piecewise constant demand with $O(k^2)$ complexity and no-regret learning guarantees, together with a linear-setting analysis that yields tractable policy structure. A central conceptual contribution is the modified demand elasticity, which captures how engagement dynamics and friction shape optimal policies and alignment between platform incentives and user welfare. The results reveal counterintuitive effects, such as friction potentially increasing engagement under optimal strategies, with implications for the design and evaluation of recommender systems and platform competition.

Abstract

Digital services face a fundamental trade-off in content selection: they must balance the immediate revenue gained from high-reward content against the long-term benefits of maintaining user engagement. Traditional multi-armed bandit models assume that users remain perpetually engaged, failing to capture the possibility that users may disengage when dissatisfied, thereby reducing future revenue potential. In this work, we introduce a model for the content selection problem that explicitly accounts for variable user engagement and disengagement. In our framework, content that maximizes immediate reward is not necessarily optimal in terms of fostering sustained user engagement. Our contributions are twofold. First, we develop computational and statistical methods for offline optimization and online learning of content selection policies. For users whose engagement patterns are defined by $k$ distinct levels, we design a dynamic programming algorithm that computes the exact optimal policy in $O(k^2)$ time. Moreover, we derive no-regret learning guarantees for an online learning setting in which the platform serves a series of users with unknown and potentially adversarial engagement patterns. Second, we introduce the concept of modified demand elasticity which captures how small changes in a user's overall satisfaction affect the platform's ability to secure long-term revenue. This notion generalizes classical demand elasticity by incorporating the dynamics of user re-engagement, thereby revealing key insights into the interplay between engagement and revenue. Notably, our analysis uncovers a counterintuitive phenomenon: although higher friction (i.e., a reduced likelihood of re-engagement) typically lowers overall revenue, it can simultaneously lead to higher user engagement under optimal content selection policies.

Figures (4)

• Figure 4.1: Plot of the function $h(p) \coloneqq \frac{1}{1 - \gamma p} - \frac{\gamma}{1-\gamma}p$ on the domain $p \in [0, 1]$ for various choices of $\gamma$.
• Figure 4.2: Asymptotic app utility at different levels of user demand and friction. Content revenue and the app creator's discount factor are fixed at $\mathop{\mathrm{\mathbb{E}}}\limits\left[R_i\right] = 1$ and $\gamma = 0.9$ for clarity.
• Figure 4.3: The ratio of the factors (A), (B), and (C) that compose $\tfrac{\partial}{\partial x} \tfrac{1}{1 - \gamma \widetilde{f}(x)}$ as stated in \ref{['eq:factors']} when there is full friction ($c = 1$) against when there is no friction ($c = 0$). The app creator's discount factor is fixed at $\gamma = 0.9$.
• Figure 4.4: Ratio of modified demand elasticity $\frac{d}{dx} \log \widetilde{f}(x)$ to classical demand elasticity $\frac{d}{dx} \log f(x)$.

Theorems & Definitions (86)

• Lemma 2.0
• Theorem 2.1
• proof
• Lemma 3.0
• Lemma 3.0
• Theorem 3.1
• proof
• Lemma 3.1
• Lemma 3.1
• Theorem 3.2