  Modern socio-technical systems typically consist of many interconnected users
and competing service providers, where notions like market equilibrium are
tightly connected to the ``evolution'' of the network of users. In this paper,
we model the users' dynamics as a linear dynamical system, and the service
providers as agents taking part to a generalized Nash game, whose outcome
coincides with the input of the users' dynamics. We thus characterize the
notion of co-evolution of the market and the network dynamics and derive
dissipativity-based conditions leading to a pertinent notion of equilibrium. We
then focus on the control design and adopt the light-touch policy to
incentivize or penalize the service providers as little as possible, while
steering the networked system to a desirable outcome. We also provide a
dimensionality-reduction procedure, which offers network-size independent
conditions. Finally, we illustrate our novel notions and algorithms on a
simulation setup stemming from digital market regulations for influencers, a
topic of growing interest.
