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Modern socio-technical systems typically consist of many interconnected usersand competing service providers, where notions like market equilibrium aretightly connected to the ``evolution'' of the network of users. In this paper,we model the users' dynamics as a linear dynamical system, and the serviceproviders as agents taking part to a generalized Nash game, whose outcomecoincides with the input of the users' dynamics. We thus characterize thenotion of co-evolution of the market and the network dynamics and derivedissipativity-based conditions leading to a pertinent notion of equilibrium. Wethen focus on the control design and adopt the light-touch policy toincentivize or penalize the service providers as little as possible, whilesteering the networked system to a desirable outcome. We also provide adimensionality-reduction procedure, which offers network-size independentconditions. Finally, we illustrate our novel notions and algorithms on asimulation setup stemming from digital market regulations for influencers, atopic of growing interest.

Incentives and co-evolution: Steering linear dynamical systems with noncooperative agents