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

Content creators compete for exposure on recommendation platforms, and such strategic behavior leads to a dynamic shift over the content distribution. However, how the creators' competition impacts user welfare and how the relevance-driven recommendation influences the dynamics in the long run are still largely unknown. This work provides theoretical insights into these research questions. We model the creators' competition under the assumptions that: 1) the platform employs an innocuous top-$K$ recommendation policy; 2) user decisions follow the Random Utility model; 3) content creators compete for user engagement and, without knowing their utility function in hindsight, apply arbitrary no-regret learning algorithms to update their strategies. 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 myopic approach to the recommendation, i.e., relevance-driven matching performs reasonably well in the long run, as long as users' decisions involve randomness and the platform provides reasonably many alternatives to its users.