Distributed convergence to Nash equilibria in network and average aggregative games



Francesca Parise, Sergio Grammatico, Basilio Gentile, John Lygeros


IFAC Automatica


We use network aggregative games to model populations of selfish agents that interact through a network. Specifically, we examine games where each player minimizes a 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. Firstly, we propose a new class of distributed algorithms to steer the strategies of the rational agents to a Nash equilibrium configuration, with guaranteed convergence under different sufficient conditions depending on the cost functions and on the network. Secondly, we show that the newly introduced network aggregative game framework, combined with consensus theory, can also be used to recover a Nash equilibrium of average aggregative games in a distributed fashion, that is, without requiring the presence of a central coordinator. Our theoretical findings allow us to extend previous literature results on two different classes of applications: multi-dimensional, convex-constrained opinion dynamics and demand-response schemes for energy management.