  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.
