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We consider network aggregative games to model and study multi-agentpopulations in which each rational agent is influenced by the aggregatebehavior of its neighbors, as specified by an underlying network. Specifically,we examine systems where each agent minimizes a quadratic cost function, thatdepends on its own strategy and on a convex combination of the strategies ofits neighbors, and is subject to personalized convex constraints. We analyzethe best response dynamics and we propose alternative distributed algorithms tosteer the strategies of the rational agents to a Nash equilibriumconfiguration. The convergence of these schemes is guaranteed under differentsufficient conditions, depending on the matrices defining the cost and on thenetwork. Additionally, we propose an extension to the network aggregative gamesetting that allows for multiple rounds of communications among the agents, andwe illustrate how it can be combined with consensus theory to recover asolution to the mean field control problem in a distributed fashion, that is,without requiring the presence of a central coordinator. Finally, we apply ourtheoretical findings to study a novel multi-dimensional, convex-constrainedmodel of opinion dynamics and a hierarchical demand-response scheme for energymanagement in smart buildings, extending literature results.

Network Aggregative Games and Distributed Mean Field Control via Consensus Theory