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Content creators compete for exposure on recommendation platforms, and suchstrategic behavior leads to a dynamic shift over the content distribution.However, how the creators' competition impacts user welfare and how therelevance-driven recommendation influences the dynamics in the long run arestill largely unknown.  This work provides theoretical insights into these research questions. Wemodel the creators' competition under the assumptions that: 1) the platformemploys an innocuous top-$K$ recommendation policy; 2) user decisions followthe Random Utility model; 3) content creators compete for user engagement and,without knowing their utility function in hindsight, apply arbitrary no-regretlearning algorithms to update their strategies. We study the user welfareguarantee through the lens of Price of Anarchy and show that the fraction ofuser welfare loss due to creator competition is always upper bounded by a smallconstant depending on $K$ and randomness in user decisions; we also prove thetightness of this bound. Our result discloses an intrinsic merit of the myopicapproach to the recommendation, i.e., relevance-driven matching performsreasonably well in the long run, as long as users' decisions involve randomnessand the platform provides reasonably many alternatives to its users.

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