  We consider network aggregative games to model and study multi-agent
populations in which each rational agent is influenced by the aggregate
behavior of its neighbors, as specified by an underlying network. Specifically,
we examine systems where each agent minimizes a quadratic cost function, that
depends on its own strategy and on a convex combination of the strategies of
its neighbors, and is subject to personalized convex constraints. We analyze
the best response dynamics and we propose alternative distributed algorithms to
steer the strategies of the rational agents to a Nash equilibrium
configuration. The convergence of these schemes is guaranteed under different
sufficient conditions, depending on the matrices defining the cost and on the
network. Additionally, we propose an extension to the network aggregative game
setting that allows for multiple rounds of communications among the agents, and
we illustrate how it can be combined with consensus theory to recover a
solution to the mean field control problem in a distributed fashion, that is,
without requiring the presence of a central coordinator. Finally, we apply our
theoretical findings to study a novel multi-dimensional, convex-constrained
model of opinion dynamics and a hierarchical demand-response scheme for energy
management in smart buildings, extending literature results.
