Incentives and Coevolution: Steering Linear Dynamical Systems with Noncooperative Agents

Modern sociotechnical 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 article, we model the users' dynamics as a linear dynamical system and the service providers as agents taking part in a generalized Nash game, whose outcome coincides with the input of the users' dynamics. We thus characterize the notion of coevolution 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.