Producers Equilibria and Dynamics in Engagement-Driven Recommender Systems

Krishna Acharya, Juba Ziani, Jingyan Wang, Varun Vangala

Abstract: Online platforms such as YouTube, Instagram heavily rely on recommender systems to decide what content to present to users. Producers, in turn, often create content that is likely to be recommended to users and have users engage with it. To do so, producers try to align their content with the preferences of their targeted user base. In this work, we explore the equilibrium behavior of producers who are interested in maximizing user engagement. We study two variants of the content-serving rule for the platform's recommender system, and provide a structural characterization of producer behavior at equilibrium: namely, each producer chooses to focus on a single embedded feature. We further show that specialization, defined as different producers optimizing for distinct types of content, naturally emerges from the competition among producers trying to maximize user engagement. We provide a heuristic for computing equilibria of our engagement game, and evaluate it experimentally. We highlight i) the performance and convergence of our heuristic, ii) the degree of producer specialization, and iii) the impact of the content-serving rule on producer and user utilities at equilibrium and provide guidance on how to set the content-serving rule.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

**Additional Serving Rules**
We have incorporated the Top-k softmax and round-robin serving rules as additional baselines. Formal descriptions of these serving rules have been added to Section 2.

**Sparse Dataset**
To evaluate performance on sparse features, we constructed a sparse synthetic dataset by generating user embeddings uniformly at random over the probability simplex and applying an element-wise masking operation. The masking uses random Boolean vectors with 90% of the values set to zero.

**Figure 1 (Section 5)**
Updated to include results for larger embedding dimensions ($d=50$ and $d=100$). The figure demonstrates that the number of iterations required to reach Nash equilibrium scales linearly, highlighting the low asymptotic complexity of Algorithm 1.

**Table 1**
Updated to show the number of converged instances across serving rules(Softmax, Top-10 softmax, Top-20 softmax, greedy, linear and round-robin) for the Movielens-100k dataset. The results indicate that "greedier'' serving rules generally result in fewer converged instances.

**Figure 4b (Section 5)**
Added to illustrate the average producer utility across all serving rules for the Movielens-100k dataset. Key observation: Lower temperatures and smaller top-k values lead to higher producer utility, but at the expense of reduced convergence to Nash equilibrium as seen in Table 1.

**Figures 6 and 7 (Appendix C)**
Present producer distributions for the Top-20 softmax; greedy, and round-robin serving rules, providing further insights into producer specialization.

**Appendix E** Figure 12: Shows producer specialization for the sparse dataset, with lower softmax temperatures resulting in greater producer specialization, consistent with previous findings.

Figure 11: Plots the average producer utility across serving rules for the sparse dataset, with similar insights as Figure 4b.

Code: https://github.com/krishnacharya/recsys_eq

Assigned Action Editor: ~Manuel_Gomez_Rodriguez1

Submission Number: 3758