MODELING CONTENT CREATOR INCENTIVES ON ALGORITHM-CURATED PLATFORMS

Abstract

Content creators compete for user attention. Their reach crucially depends on algorithmic choices made by developers on online platforms. To maximize exposure, many creators adapt strategically, as evidenced by examples like the sprawling search engine optimization industry. This begets competition for the finite user attention pool. We formalize these dynamics in what we call an exposure game, a model of incentives induced by algorithms, including modern factorization and (deep) two-tower architectures. We prove that seemingly innocuous algorithmic choices-e.g., non-negative vs. unconstrained factorization-significantly affect the existence and character of (Nash) equilibria in exposure games. We proffer use of creator behavior models, like exposure games, for an (ex-ante) predeployment audit. Such an audit can identify misalignment between desirable and incentivized content, and thus complement post-hoc measures like content filtering and moderation. To this end, we propose tools for numerically finding equilibria in exposure games, and illustrate results of an audit on the MovieLens and LastFM datasets. Among else, we find that the strategically produced content exhibits strong dependence between algorithmic exploration and content diversity, and between model expressivity and bias towards gender-based user and creator groups.

1. INTRODUCTION

In 2018, Jonah Peretti (CEO, Buzzfeed) raised alarm when a Facebook main feed update started boosting junk and divisive content (Hagey & Horwitz, 2021) . In Poland, the same update caused an uptick in negative political messaging (Hagey & Horwitz, 2021) . Tailoring content to algorithms is not unique to social media. For example, some search engine optimization (SEO) professionals specialize on managing impacts of Google Search updates (Marentis, 2014; Dennis, 2016; Shahzad et al., 2020; Patil et al., 2021; Goodwin, 2021) . While motivations for adapting content range from economic to socio-political, they often translate into the same operative goal: exposure maximization. We study how algorithms affect exposuremaximizing content creators. We propose a novel incentive-based behavior model called an exposure game, where producers compete for a finite user attention pool by crafting content ranked highly by a given algorithm (Section 1.1). When producers act strategically, a steady state-Nash equilibrium (NE)-may be reached, with no one able to unilaterally improve their exposure (utility). The content produced in a NE can thus be interpreted as what the algorithm implicitly incentivizes. We focus on algorithms which model user preferences as an inner product of d-dimensional user and item embeddings, and rank items by the estimated preference. Section 2 presents theoretical results on the NE induced by these algorithms. We identify cases where algorithmic changes seemingly unconnected to producer incentives-e.g., switching from non-negative to unconstrained embeddings-determine whether there are zero, one, or multiple NE. The character of NE is also affected by the level of algorithmic exploration. Perhaps counter-intuitively, we show that high levels of exploration incentivize broadly appealing content, whereas low levels lead to specialization. In Section 3, we explore how creator behavior models can facilitate a pre-deployment audit. Such an audit could be particularly useful for assessing the producer impact of algorithmic changes, which is hard to measure by A/B testing for two important reasons: (1) producers cannot be easily randomized to distinct treatment groups, and (2) there is often a delay between deployment and content adaptation. Our hope is that this new style of auditing will enable detection of misalignment between the induced and desired incentives, and thus flag issues to either immediately address, or monitor in content filtering and moderation. For demonstration, we execute a pre-deployment audit on the MovieLens and LastFM datasets using the exposure game behavior model, and matrix factorization based recommenders. We find a strong dependence between algorithmic choices like embedding dimension and level of exploration, and properties of the incetivized content such as diversity (confirming our theory), and targeting of gender-based user and creator groups.

1.1. SETTING AND THE EXPOSURE GAME INCENTIVE MODEL

We assume there is a fixed recommender system trained on past data, and a fixed population of users (consumers). Together, these induce a demand distribution P c which represents typical traffic on the platform over a predefined period of time. Content is created by n ∈ N producers who try to maximize their expected exposure (utility). Denoting consumers by c ∼ P c , an item created by the i th producer by s i (strategy), s := (s i ) i∈[n] , and s \i := (s j ) j̸ =i , we define (expected) exposure as the proportion of the "user attention pool" captured by the i th producer u i (s) = u i (s i , s \i ) := E c∼Pc [1{c is exposed to s i }] ⋆ = E c∼Pc [p i (c)] , with p i (c) ≥ 0 the probability that the algorithm exposes c to s i rather than any s \i . As common in game theory, we can extend from deterministic single item strategies to stochastic multi-item strategies s i ∼ P i for some distribution P i . This extension is discussed in more detail in Section 2. The assumption that E[1{c is exposed to s i }] ⋆ = E[p i (c)] does not explicitly model interactions not mediated by the algorithm (e.g., YouTube videos linked to by an external website). This may be a reasonable approximation for infinite feed platforms (e.g., Twitter, Facebook, TikTok) where most consumers scroll through items in the algorithm-defined order, and search engines (e.g., Google, Bing) where first-page bias is well documented (Craswell et al., 2008) . While similar assumptions are common in the literature (e.g., Li et al., 2010; Chen et al., 2019; Ben-Porat et al., 2020; Curmei et al., 2021) , alternative interaction models are an important future research direction. Unlike previous work (Section 1.2), we focus on the popular class of factorization-based algorithms. These models rank items by a score estimated by the inner product of user and item embeddings c, s i ∈ R d . The larger this score, the higher the probability of exposure, which we model as p i (c) = exp(τ -1 ⟨c, s i ⟩) n i ′ =1 exp(τ -1 ⟨c, s i ′ ⟩) = softmax τ -1 ⟨c, s i ′ ⟩ n i ′ =1 i , where τ ≥ 0 is a temperature parameter which controls the spread of exposure probabilities over the top scoring items. When τ = 0 (i.e., hardmax), these probabilities correspond to top-1 recommendation or absolute first-position bias. Taking τ > 0 models the effects of ranked position, injected randomness for exploration, and can partially adjust for user randomness and other factors which make top-ranked items receive more but not all of the traffic. While an approximation in some settings, Equation (2) has been directly used, e.g., by YouTube (Chen et al., 2019) . We emphasize that we make no assumption on how the embeddings are obtained. Our conclusions thus apply equally to classical matrix factorization and deep learning-based systems. We are now ready to formalize exposure games, an incentive-based model of creator behavior. We restrict items s i to the unit sphere S d-foot_0 . A norm constraint is necessary as otherwise exposure could be maximized by inflating ∥s i ∥ → ∞, which is not observed in practice. 1 We distinguish



Possibly due to the often finite rating scale, use of gradient clipping, and various forms of regularization.



Figure 1: Exposure game. Items s i ∈ S d-1 placed to maximize exposure to consumers c ∼ P c .

An exposure game consists of an embedding dimension d ∈ N, a demand distribution P c ∈ P(R d ), and n ∈ N producers, each of whom chooses a strategy s i ∈ S d-1 = {v ∈ R d : ∥v∥ = 1}, to maximize their utility u i (s) = E c∼Pc [p i (c)] with p i (c) as in Equation (2) for a given τ ≥ 0.

