  Recommendation systems are extremely popular tools for matching users and
contents. However, when content providers are strategic, the basic principle of
matching users to the closest content, where both users and contents are
modeled as points in some semantic space, may yield low social welfare. This is
due to the fact that content providers are strategic and optimize their offered
content to be recommended to as many users as possible. Motivated by modern
applications, we propose the widely studied framework of facility location
games to study recommendation systems with strategic content providers. Our
conceptual contribution is the introduction of a $\textit{mediator}$ to
facility location models, in the pursuit of better social welfare. We aim at
designing mediators that a) induce a game with high social welfare in
equilibrium, and b) intervene as little as possible. In service of the latter,
we introduce the notion of $\textit{intervention cost}$, which quantifies how
much damage a mediator may cause to the social welfare when an off-equilibrium
profile is adopted. As a case study in high-welfare low-intervention mediator
design, we consider the one-dimensional segment as the user domain. We propose
a mediator that implements the socially optimal strategy profile as the unique
equilibrium profile, and show a tight bound on its intervention cost.
Ultimately, we consider some extensions, and highlight open questions for the
general agenda.
