  Online platforms such as YouTube or Instagram heavily rely on recommender
systems to decide what content to show to which users. Producers often aim to
produce content that is likely to be shown to users and have the users engage.
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
different types of content, naturally arises 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 how i) the performance and convergence of our heuristic, ii) the
level of producer specialization, and iii) the producer and user utilities at
equilibrium are affected by the choice of content-serving rule and provide
guidance on how to set the content-serving rule to use in engagement games.
