  Algorithmic recommender systems such as Spotify and Netflix affect not only
consumer behavior but also producer incentives. Producers seek to create
content that will be shown by the recommendation algorithm, which can impact
both the diversity and quality of their content. In this work, we investigate
the resulting supply-side equilibria in personalized content recommender
systems. We model users and content as $D$-dimensional vectors, the
recommendation algorithm as showing each user the content with highest dot
product, and producers as maximizing the number of users who are recommended
their content minus the cost of production. Two key features of our model are
that the producer decision space is multi-dimensional and the user base is
heterogeneous, which contrasts with classical low-dimensional models.
  Multi-dimensionality and heterogeneity create the potential for
specialization, where different producers create different types of content at
equilibrium. Using a duality argument, we derive necessary and sufficient
conditions for whether specialization occurs: these conditions depend on the
extent to which users are heterogeneous and to which producers can perform well
on all dimensions at once without incurring a high cost. Then, we characterize
the distribution of content at equilibrium in concrete settings with two
populations of users. Lastly, we show that specialization can enable producers
to achieve positive profit at equilibrium, which means that specialization can
reduce the competitiveness of the marketplace. At a conceptual level, our
analysis of supply-side competition takes a step towards elucidating how
personalized recommendations shape the marketplace of digital goods, and
towards understanding what new phenomena arise in multi-dimensional competitive
settings.
