How Bad is Top-$K$ Recommendation under Competing Content Creators?

This study explores the impact of content creators' competition on user welfare in recommendation platforms, as well as the long-term dynamics of relevance-driven recommendations. We establish a model of creator competition, under the setting where the platform uses a top-$K$ recommendation policy, user decisions are guided by the Random Utility model, and creators, in absence of explicit utility functions, employ arbitrary no-regret learning algorithms for strategy updates. We study the user welfare guarantee through the lens of Price of Anarchy and show that the fraction of user welfare loss due to creator competition is always upper bounded by a small constant depending on $K$ and randomness in user decisions; we also prove the tightness of this bound. Our result discloses an intrinsic merit of the relevance-driven recommendation policy, as long as users' decisions involve randomness and the platform provides reasonably many alternatives to its users.